=2(x^2+4x-360)

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Solution for =2(x^2+4x-360) equation: 


Simplifying
0 = 2(x2 + 4x + -360)

Reorder the terms:
0 = 2(-360 + 4x + x2)
0 = (-360 * 2 + 4x * 2 + x2 * 2)
0 = (-720 + 8x + 2x2)

Solving
0 = -720 + 8x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 720 = 720
720 + -8x + -2x2 = -720 + 8x + 2x2 + 720 + -8x + -2x2

Reorder the terms:
720 + -8x + -2x2 = -720 + 720 + 8x + -8x + 2x2 + -2x2

Combine like terms: -720 + 720 = 0
720 + -8x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
720 + -8x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
720 + -8x + -2x2 = 0 + 2x2 + -2x2
720 + -8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
720 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(360 + -4x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(360 + -4x + -1x2)' equal to zero and attempt to solve:

Simplifying
360 + -4x + -1x2 = 0

Solving
360 + -4x + -1x2 = 0

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

Divide each side by '-1'.
-360 + 4x + x2 = 0

Move the constant term to the right:

Add '360' to each side of the equation.
-360 + 4x + 360 + x2 = 0 + 360

Reorder the terms:
-360 + 360 + 4x + x2 = 0 + 360

Combine like terms: -360 + 360 = 0
0 + 4x + x2 = 0 + 360
4x + x2 = 0 + 360

Combine like terms: 0 + 360 = 360
4x + x2 = 360

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 = 360 + 4

Reorder the terms:
4 + 4x + x2 = 360 + 4

Combine like terms: 360 + 4 = 364
4 + 4x + x2 = 364

Factor a perfect square on the left side:
(x + 2)(x + 2) = 364

Calculate the square root of the right side: 19.078784028

Break this problem into two subproblems by setting 
(x + 2) equal to 19.078784028 and -19.078784028.


Subproblem 1
x + 2 = 19.078784028

Simplifying
x + 2 = 19.078784028

Reorder the terms:
2 + x = 19.078784028

Solving
2 + x = 19.078784028

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 = 19.078784028 + -2

Combine like terms: 2 + -2 = 0
0 + x = 19.078784028 + -2
x = 19.078784028 + -2

Combine like terms: 19.078784028 + -2 = 17.078784028
x = 17.078784028

Simplifying
x = 17.078784028


Subproblem 2
x + 2 = -19.078784028

Simplifying
x + 2 = -19.078784028

Reorder the terms:
2 + x = -19.078784028

Solving
2 + x = -19.078784028

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 = -19.078784028 + -2

Combine like terms: 2 + -2 = 0
0 + x = -19.078784028 + -2
x = -19.078784028 + -2

Combine like terms: -19.078784028 + -2 = -21.078784028
x = -21.078784028

Simplifying
x = -21.078784028


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.078784028, -21.078784028}
Solution
x = {17.078784028, -21.078784028}

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