2(x^2+8x-133)=0

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Solution for 2(x^2+8x-133)=0 equation: 


Simplifying
2(x2 + 8x + -133) = 0

Reorder the terms:
2(-133 + 8x + x2) = 0
(-133 * 2 + 8x * 2 + x2 * 2) = 0
(-266 + 16x + 2x2) = 0

Solving
-266 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-133 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-133 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-133 + 8x + x2 = 0

Solving
-133 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '133' to each side of the equation.
-133 + 8x + 133 + x2 = 0 + 133

Reorder the terms:
-133 + 133 + 8x + x2 = 0 + 133

Combine like terms: -133 + 133 = 0
0 + 8x + x2 = 0 + 133
8x + x2 = 0 + 133

Combine like terms: 0 + 133 = 133
8x + x2 = 133

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 = 133 + 16

Reorder the terms:
16 + 8x + x2 = 133 + 16

Combine like terms: 133 + 16 = 149
16 + 8x + x2 = 149

Factor a perfect square on the left side:
(x + 4)(x + 4) = 149

Calculate the square root of the right side: 12.206555616

Break this problem into two subproblems by setting 
(x + 4) equal to 12.206555616 and -12.206555616.


Subproblem 1
x + 4 = 12.206555616

Simplifying
x + 4 = 12.206555616

Reorder the terms:
4 + x = 12.206555616

Solving
4 + x = 12.206555616

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 = 12.206555616 + -4

Combine like terms: 4 + -4 = 0
0 + x = 12.206555616 + -4
x = 12.206555616 + -4

Combine like terms: 12.206555616 + -4 = 8.206555616
x = 8.206555616

Simplifying
x = 8.206555616


Subproblem 2
x + 4 = -12.206555616

Simplifying
x + 4 = -12.206555616

Reorder the terms:
4 + x = -12.206555616

Solving
4 + x = -12.206555616

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 = -12.206555616 + -4

Combine like terms: 4 + -4 = 0
0 + x = -12.206555616 + -4
x = -12.206555616 + -4

Combine like terms: -12.206555616 + -4 = -16.206555616
x = -16.206555616

Simplifying
x = -16.206555616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.206555616, -16.206555616}
Solution
x = {8.206555616, -16.206555616}

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