2(x^2+8x-960)=0

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Solution for 2(x^2+8x-960)=0 equation: 


Simplifying
2(x2 + 8x + -960) = 0

Reorder the terms:
2(-960 + 8x + x2) = 0
(-960 * 2 + 8x * 2 + x2 * 2) = 0
(-1920 + 16x + 2x2) = 0

Solving
-1920 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-960 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-960 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-960 + 8x + x2 = 0

Solving
-960 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '960' to each side of the equation.
-960 + 8x + 960 + x2 = 0 + 960

Reorder the terms:
-960 + 960 + 8x + x2 = 0 + 960

Combine like terms: -960 + 960 = 0
0 + 8x + x2 = 0 + 960
8x + x2 = 0 + 960

Combine like terms: 0 + 960 = 960
8x + x2 = 960

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 960 + 16

Reorder the terms:
16 + 8x + x2 = 960 + 16

Combine like terms: 960 + 16 = 976
16 + 8x + x2 = 976

Factor a perfect square on the left side:
(x + 4)(x + 4) = 976

Calculate the square root of the right side: 31.240998704

Break this problem into two subproblems by setting 
(x + 4) equal to 31.240998704 and -31.240998704.


Subproblem 1
x + 4 = 31.240998704

Simplifying
x + 4 = 31.240998704

Reorder the terms:
4 + x = 31.240998704

Solving
4 + x = 31.240998704

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 31.240998704 + -4

Combine like terms: 4 + -4 = 0
0 + x = 31.240998704 + -4
x = 31.240998704 + -4

Combine like terms: 31.240998704 + -4 = 27.240998704
x = 27.240998704

Simplifying
x = 27.240998704


Subproblem 2
x + 4 = -31.240998704

Simplifying
x + 4 = -31.240998704

Reorder the terms:
4 + x = -31.240998704

Solving
4 + x = -31.240998704

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -31.240998704 + -4

Combine like terms: 4 + -4 = 0
0 + x = -31.240998704 + -4
x = -31.240998704 + -4

Combine like terms: -31.240998704 + -4 = -35.240998704
x = -35.240998704

Simplifying
x = -35.240998704


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.240998704, -35.240998704}
Solution
x = {27.240998704, -35.240998704}

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