2(x^2-12x-40)=0

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Solution for 2(x^2-12x-40)=0 equation: 


Simplifying
2(x2 + -12x + -40) = 0

Reorder the terms:
2(-40 + -12x + x2) = 0
(-40 * 2 + -12x * 2 + x2 * 2) = 0
(-80 + -24x + 2x2) = 0

Solving
-80 + -24x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -12x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-40 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + -12x + x2 = 0

Solving
-40 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -12x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -12x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -12x + x2 = 0 + 40
-12x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-12x + x2 = 40

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 40 + 36

Reorder the terms:
36 + -12x + x2 = 40 + 36

Combine like terms: 40 + 36 = 76
36 + -12x + x2 = 76

Factor a perfect square on the left side:
(x + -6)(x + -6) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(x + -6) equal to 8.717797887 and -8.717797887.


Subproblem 1
x + -6 = 8.717797887

Simplifying
x + -6 = 8.717797887

Reorder the terms:
-6 + x = 8.717797887

Solving
-6 + x = 8.717797887

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 8.717797887 + 6

Combine like terms: -6 + 6 = 0
0 + x = 8.717797887 + 6
x = 8.717797887 + 6

Combine like terms: 8.717797887 + 6 = 14.717797887
x = 14.717797887

Simplifying
x = 14.717797887


Subproblem 2
x + -6 = -8.717797887

Simplifying
x + -6 = -8.717797887

Reorder the terms:
-6 + x = -8.717797887

Solving
-6 + x = -8.717797887

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -8.717797887 + 6

Combine like terms: -6 + 6 = 0
0 + x = -8.717797887 + 6
x = -8.717797887 + 6

Combine like terms: -8.717797887 + 6 = -2.717797887
x = -2.717797887

Simplifying
x = -2.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.717797887, -2.717797887}
Solution
x = {14.717797887, -2.717797887}

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