How to solve 5x^2-3x=25 by completing the square?

rehaucesnwr1

rehaucesnwr1

Answered question

2023-02-22

How to solve 5 x 2 - 3 x = 25 by completing the square?

Answer & Explanation

Jayden Landry

Jayden Landry

Beginner2023-02-23Added 7 answers

So solution:
5 x 2 - 3 x = 25 or 5 ( x 2 - 3 5 x ) = 25
5 ( x 2 - 3 5 x + 9 100 ) = 25 + 9 20
5 ( x - 3 10 ) 2 = 509 20
( x - 3 10 ) 2 = 509 100
( x - 3 10 ) 2 = 509 100
x = 0.3 ± 2.256 x = 2.556 , x = - 1.956
Result: x 2.556 , x - 1.956
Libby Fernandez

Libby Fernandez

Beginner2023-02-24Added 5 answers

Here is an example of how to solve using the difference of squares identity, premultiplying by 20 to reduce the number of fractions, and completing the square:
a 2 - b 2 = ( a - b ) ( a + b )
with #a=(10x-3)# and #b=sqrt(509)#
We have:
5 x 2 - 3 x = 25
25 from each side is subtracted to yield:
5 x 2 - 3 x - 25 = 0
Multiply by 20 = 5 2 2 to make the leading term a perfect square and the middle term divisible by 2...
Therefore:
0 = 20 ( 5 x 2 - 3 x - 25 )
0 = 100 x 2 - 60 x - 500
0 = ( 10 x ) 2 - 2 ( 10 x ) ( 3 ) + 3 2 - 509
0 = ( 10 x - 3 ) 2 - ( 509 ) 2
0 = ( ( 10 x - 3 ) - 509 ) ( ( 10 x - 3 ) + 509 )
0 = ( 10 x - 3 - 509 ) ( 10 x - 3 + 509 )
Hence:
10 x = 3 ± 509
So:
x = 3 10 ± 509 10

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