x^2-16x-136=0

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Solution for x^2-16x-136=0 equation: 


Simplifying
x2 + -16x + -136 = 0

Reorder the terms:
-136 + -16x + x2 = 0

Solving
-136 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '136' to each side of the equation.
-136 + -16x + 136 + x2 = 0 + 136

Reorder the terms:
-136 + 136 + -16x + x2 = 0 + 136

Combine like terms: -136 + 136 = 0
0 + -16x + x2 = 0 + 136
-16x + x2 = 0 + 136

Combine like terms: 0 + 136 = 136
-16x + x2 = 136

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 136 + 64

Reorder the terms:
64 + -16x + x2 = 136 + 64

Combine like terms: 136 + 64 = 200
64 + -16x + x2 = 200

Factor a perfect square on the left side:
(x + -8)(x + -8) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(x + -8) equal to 14.142135624 and -14.142135624.


Subproblem 1
x + -8 = 14.142135624

Simplifying
x + -8 = 14.142135624

Reorder the terms:
-8 + x = 14.142135624

Solving
-8 + x = 14.142135624

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 14.142135624 + 8

Combine like terms: -8 + 8 = 0
0 + x = 14.142135624 + 8
x = 14.142135624 + 8

Combine like terms: 14.142135624 + 8 = 22.142135624
x = 22.142135624

Simplifying
x = 22.142135624


Subproblem 2
x + -8 = -14.142135624

Simplifying
x + -8 = -14.142135624

Reorder the terms:
-8 + x = -14.142135624

Solving
-8 + x = -14.142135624

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -14.142135624 + 8

Combine like terms: -8 + 8 = 0
0 + x = -14.142135624 + 8
x = -14.142135624 + 8

Combine like terms: -14.142135624 + 8 = -6.142135624
x = -6.142135624

Simplifying
x = -6.142135624


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.142135624, -6.142135624}

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