Solve the equation algebraically. Verify your results using a graphing

Gregory Jones

Gregory Jones

Answered question

2021-12-21

Solve the equation algebraically. Verify your results using a graphing utility.
x(1+2x)=(2x1)(x2)

Answer & Explanation

Cassandra Ramirez

Cassandra Ramirez

Beginner2021-12-22Added 30 answers

Step 1
According to the distributive property of multiplication, a(b+c)=ab+ac or (a+b)(c+d)=ac+ad+bc+bd.
Simplify both the sides of the equation using the distributive property of multiplication as follows:
x(1+2x)=(2x1)(x2)
x+2x2=2x24xx+2
x+2x2=2x25x+2
Step 2
Add 5x2x2 to both the sides of the equation and then divide both the sides of the equation by 6 to solve for x.
x+2x2+5x2x2=2x25x+2+5x2x2
6x=2
x=13
Step 3
Input the equation x(1+2x)=(2x1)(x2) in the graphing utility and solve for x.
The value of x obtained is 13.
Hence, the result is verified.
Joseph Fair

Joseph Fair

Beginner2021-12-23Added 34 answers

x(1+2x)=(2x1)(x2)
x(2x+1)=(2x1)(x2)
2x2+x=(2x1)(x2)
2x2+x=2x(x2)1(x2)
2x2+x=2x24x1(x2)
2x2+x=2x24xx+2
2x2+x=2x25x+2
2x2+x(2x25x+2)=0
2x2+x2x2+5x2=0
x+5x2=0
6x2=0
6x2+2=0+2
6x=2
6x6=26
x=13
nick1337

nick1337

Expert2021-12-28Added 777 answers

x(1+2x)=(2x1)(x2)
1) Rearrange the terms of the equation
x(2x+1)=(2x1)(x2)
2) Open parenthesis
2x2+x=(2x1)(x2)
3) Open parenthesis
2x2+x=2x(x2)1(x2)
4) Open parenthesis
2x2+x=2x24x1(x2)
5) Open parenthesis
2x2+x=2x24xx+2
6) Combine similar members
2x2+x=2x25x+2
7) Move conditions to the left
2x2+x(2x25x+2)=0
8) Open parenthesis
2x2+x2x2+5x2=0
9) Combine similar members
x+5x2=0
10) Combine similar members
6x2=0
11) Add 2 to both sides of the equation
6x2+2=0+2
12) Simplify
6x=2
13) Divide both sides of the equation by the same term
6x6=26
14) Simplify
x=13

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