Which rules are used to make function like one in Laplace Transformations table?I have function like this: s 2 + 3 s + 3 ( 2 s 2 + 7 s + 7 ) It needs to be brought to the level of Laplace Transformations from table, like these two: a ( s − b ) 2 + a 2 s − b ( s − b ) 2 + a 2 I have the solution for this problem, but I can't figure out the logic behind it. Steps included are: 1 2 − 0.5 s + 0.5 2 s 2 + 7 s + 7 = 1 2 − 0.5 s + 0.5 ( s + 1.75 ) 2 + 0.6614 2 = 1 2 − 0.5 ∗ s + 1.75 ( s + 1.75 ) 2 + 0.6614 2 + ( 0.5 ∗ 1.75 − 0.5 ) ∗ 1 0.6614 ∗ 0.6614 ( s + 1.75 ) 2 + 0.6614 2

Question

Which rules are used to make function like one in Laplace Transformations table?I have function like this:                    s        2            +      3      s      +      3              (      2              s        2            +      7      s      +      7      )      It needs to be brought to the level of Laplace Transformations from table, like these two:      a          (      s      −      b              )        2            +              a        2                        s      −      b              (      s      −      b              )        2            +              a        2            I have the solution for this problem, but I can&#039;t figure out the logic behind it. Steps included are:      1    2    −            0.5      s      +      0.5              2              s        2            +      7      s      +      7        =      1    2    −            0.5      s      +      0.5              (      s      +      1.75              )        2            +              0.6614        2              =      1    2    −  0.5  ∗            s      +      1.75              (      s      +      1.75              )        2            +              0.6614        2              +  (  0.5  ∗  1.75  −  0.5  )  ∗      1    0.6614    ∗      0.6614          (      s      +      1.75              )        2            +              0.6614        2

thoumToofwj · Accepted Answer

I have outlined the logic of the calculations step by step below. However, your solution seems to have slight problems.                                                        s              2                        +            3            s            +            3                                (            2                          s              2                        +            7            s            +            7            )                                              =                                            s              2                        +            3            s            +            s                          /                        2            −            s                          /                        2            +            3            +            1                          /                        2            −            1                          /                        2                                (            2                          s              2                        +            7            s            +            7            )                                                            =                                            s              2                        +            3            s            +            s                          /                        2            −            s                          /                        2            +            3            +            1                          /                        2                                (            2                          s              2                        +            7            s            +            7            )                          −                              s                          /                        2            +            1                          /                        2                                (            2                          s              2                        +            7            s            +            7            )                                                            =                  1          2                −                  1          2                                      s            +            1                                (            2                          s              2                        +            7            s            +            7            )                                                            =                  1          2                −                  1          4                                      s            +            1                                (                          s              2                        +            7            s                          /                        2            +            7                          /                        2            )                                                            =                  1          2                −                  1          4                                      s            +            1                                (                          s              2                        +            2            ×            7                          /                        4            ×            s            +            7                          /                        2            )                                                            =                  1          2                −                  1          4                                      s            +            1                                (                          s              2                        +            2            ×            7                          /                        4            ×            s            +            (            7                          /                        4                          )              2                        −            (            7                          /                        4                          )              2                        +            7                          /                        2            )                                                            =                  1          2                −                  1          4                                      s            +            1                                (            s            +            7                          /                        4                          )              2                        −            (            7                          /                        4                          )              2                        +            7                          /                        2            )                                                            =                  1          2                −                  1          4                                      s            +            1                                (            s            +            1.75                          )              2                        −            (            1.75                          )              2                        +            3.5                                                            =                  1          2                −                  1          4                                      s            +            1                                (            s            +            1.75                          )              2                        +            0.4375                                                            =                  1          2                −                  1          4                                      s            +            1                                (            s            +            1.75                          )              2                        +            (            0.6614                          )              2                                                                        =                  1          2                −                  1          4                                      s            +            1            +            0.75            −            0.75                                (            s            +            1.75                          )              2                        +            (            0.6614                          )              2                                                                        =                  1          2                −                  1          4                                      s            +            1.75                                (            s            +            1.75                          )              2                        +            (            0.6614                          )              2                                      +                  1          4                          0.75                      (            s            +            1.75                          )              2                        +            (            0.6614                          )              2                                                                        =                  1          2                −                  1          4                                      s            +            1.75                                (            s            +            1.75                          )              2                        +            (            0.6614                          )              2                                      +                  1          4                                      0.75            ×            0.6614            ÷            0.6614                                (            s            +            1.75                          )              2                        +            (            0.6614                          )              2                                                                        =                  1          2                −                  1          4                                      s            +            1.75                                (            s            +            1.75                          )              2                        +            (            0.6614                          )              2                                      +                  1.13          4                          0.6614                      (            s            +            1.75                          )              2                        +            (            0.6614                          )              2

cricafh · Accepted Answer

s              2                        +            3            s            +            3                                (            2                          s              2                        +            7            s            +            7            )                                              =                  1          2                                      2                          s              2                        +            6            s            +            6                                (            2                          s              2                        +            7            s            +            7            )                                                                          =                  1          2                                      (            2                          s              2                        +            7            s            +            7            )            −            (            s            +            1            )                                (            2                          s              2                        +            7            s            +            7            )                                                                          =                  1          2                −                  1          2                                      s            +            1                                2                          s              2                        +            7            s            +            7                                                                          =                  1          2                −                  1          4                                      s            +            1                                              s              2                        +            (            7                          /                        2            )            s            +            (            7                          /                        2            )                                                                          =                  1          2                −                  1          4                                      s            +            1                                (            s            +            7                          /                        4                          )              2                        +            (            7                          /                        2            )            −            (            49                          /                        16            )                                                                          =                  1          2                −                  1          4                                      s            +            (            7                          /                        4            )            −            (            3                          /                        4            )                                (            s            +            7                          /                        4                          )              2                        +            7                          /                        16                                                                          =                  1          2                −                  1          4                                      s            +            7                          /                        4                                (            s            +            7                          /                        4                          )              2                        +            7                          /                        16                          +                  3          16                          1                      (            s            +            7                          /                        4                          )              2                        +            7                          /                        16                                                                          =                  1          2                −                  1          4                                      s            +            7                          /                        4                                (            s            +            7                          /                        4                          )              2                        +            7                          /                        16                          +                  3          16                          1                      (            s            +            7                          /                        4                          )              2                        +            7                          /                        16                                                                          =                  1          2                −                  1          4                                      s            +            7                          /                        4                                (            s            +            7                          /                        4                          )              2                        +                                          (                                                      7                                    4                                )                            2                                      +                  3          16                          1                      (            s            +            7                          /                        4                          )              2                        +                                          (                                                      7                                    4                                )                            2                                                                                        1          2                −                  1          4                                      s            +            7                          /                        4                                (            s            +            7                          /                        4                          )              2                        +                                          (                                                      7                                    4                                )                            2                                      +                              3                          7                                28                                                    7                        4                                (            s            +            7                          /                        4                          )              2                        +                                          (                                                      7                                    4                                )                            2

Which rules are used to make function like one in Laplace Transformations table? I have function li

Answered question

Answer & Explanation

New Questions in Pre-Algebra