2x(x+4)=396

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Solution for 2x(x+4)=396 equation: 


Simplifying
2x(x + 4) = 396

Reorder the terms:
2x(4 + x) = 396
(4 * 2x + x * 2x) = 396
(8x + 2x2) = 396

Solving
8x + 2x2 = 396

Solving for variable 'x'.

Reorder the terms:
-396 + 8x + 2x2 = 396 + -396

Combine like terms: 396 + -396 = 0
-396 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-198 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-198 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-198 + 4x + x2 = 0

Solving
-198 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '198' to each side of the equation.
-198 + 4x + 198 + x2 = 0 + 198

Reorder the terms:
-198 + 198 + 4x + x2 = 0 + 198

Combine like terms: -198 + 198 = 0
0 + 4x + x2 = 0 + 198
4x + x2 = 0 + 198

Combine like terms: 0 + 198 = 198
4x + x2 = 198

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 198 + 4

Reorder the terms:
4 + 4x + x2 = 198 + 4

Combine like terms: 198 + 4 = 202
4 + 4x + x2 = 202

Factor a perfect square on the left side:
(x + 2)(x + 2) = 202

Calculate the square root of the right side: 14.212670404

Break this problem into two subproblems by setting 
(x + 2) equal to 14.212670404 and -14.212670404.


Subproblem 1
x + 2 = 14.212670404

Simplifying
x + 2 = 14.212670404

Reorder the terms:
2 + x = 14.212670404

Solving
2 + x = 14.212670404

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 14.212670404 + -2

Combine like terms: 2 + -2 = 0
0 + x = 14.212670404 + -2
x = 14.212670404 + -2

Combine like terms: 14.212670404 + -2 = 12.212670404
x = 12.212670404

Simplifying
x = 12.212670404


Subproblem 2
x + 2 = -14.212670404

Simplifying
x + 2 = -14.212670404

Reorder the terms:
2 + x = -14.212670404

Solving
2 + x = -14.212670404

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -14.212670404 + -2

Combine like terms: 2 + -2 = 0
0 + x = -14.212670404 + -2
x = -14.212670404 + -2

Combine like terms: -14.212670404 + -2 = -16.212670404
x = -16.212670404

Simplifying
x = -16.212670404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.212670404, -16.212670404}
Solution
x = {12.212670404, -16.212670404}

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