2x+(2x+7)=x(x+23)

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Solution for 2x+(2x+7)=x(x+23) equation: 


Simplifying
2x + (2x + 7) = x(x + 23)

Reorder the terms:
2x + (7 + 2x) = x(x + 23)

Remove parenthesis around (7 + 2x)
2x + 7 + 2x = x(x + 23)

Reorder the terms:
7 + 2x + 2x = x(x + 23)

Combine like terms: 2x + 2x = 4x
7 + 4x = x(x + 23)

Reorder the terms:
7 + 4x = x(23 + x)
7 + 4x = (23 * x + x * x)
7 + 4x = (23x + x2)

Solving
7 + 4x = 23x + x2

Solving for variable 'x'.

Combine like terms: 4x + -23x = -19x
7 + -19x + -1x2 = 23x + x2 + -23x + -1x2

Reorder the terms:
7 + -19x + -1x2 = 23x + -23x + x2 + -1x2

Combine like terms: 23x + -23x = 0
7 + -19x + -1x2 = 0 + x2 + -1x2
7 + -19x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + -19x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + 19x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 19x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 19x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 19x + x2 = 0 + 7
19x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
19x + x2 = 7

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 7 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 7 + 90.25

Combine like terms: 7 + 90.25 = 97.25
90.25 + 19x + x2 = 97.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 97.25

Calculate the square root of the right side: 9.861541462

Break this problem into two subproblems by setting 
(x + 9.5) equal to 9.861541462 and -9.861541462.


Subproblem 1
x + 9.5 = 9.861541462

Simplifying
x + 9.5 = 9.861541462

Reorder the terms:
9.5 + x = 9.861541462

Solving
9.5 + x = 9.861541462

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 9.861541462 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 9.861541462 + -9.5
x = 9.861541462 + -9.5

Combine like terms: 9.861541462 + -9.5 = 0.361541462
x = 0.361541462

Simplifying
x = 0.361541462


Subproblem 2
x + 9.5 = -9.861541462

Simplifying
x + 9.5 = -9.861541462

Reorder the terms:
9.5 + x = -9.861541462

Solving
9.5 + x = -9.861541462

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -9.861541462 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -9.861541462 + -9.5
x = -9.861541462 + -9.5

Combine like terms: -9.861541462 + -9.5 = -19.361541462
x = -19.361541462

Simplifying
x = -19.361541462


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.361541462, -19.361541462}

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