x^2-26x-8=0

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Solution for x^2-26x-8=0 equation: 


Simplifying
x2 + -26x + -8 = 0

Reorder the terms:
-8 + -26x + x2 = 0

Solving
-8 + -26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -26x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -26x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -26x + x2 = 0 + 8
-26x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-26x + x2 = 8

The x term is -26x.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26x + 169 + x2 = 8 + 169

Reorder the terms:
169 + -26x + x2 = 8 + 169

Combine like terms: 8 + 169 = 177
169 + -26x + x2 = 177

Factor a perfect square on the left side:
(x + -13)(x + -13) = 177

Calculate the square root of the right side: 13.304134696

Break this problem into two subproblems by setting 
(x + -13) equal to 13.304134696 and -13.304134696.


Subproblem 1
x + -13 = 13.304134696

Simplifying
x + -13 = 13.304134696

Reorder the terms:
-13 + x = 13.304134696

Solving
-13 + x = 13.304134696

Solving for variable 'x'.

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

Add '13' to each side of the equation.
-13 + 13 + x = 13.304134696 + 13

Combine like terms: -13 + 13 = 0
0 + x = 13.304134696 + 13
x = 13.304134696 + 13

Combine like terms: 13.304134696 + 13 = 26.304134696
x = 26.304134696

Simplifying
x = 26.304134696


Subproblem 2
x + -13 = -13.304134696

Simplifying
x + -13 = -13.304134696

Reorder the terms:
-13 + x = -13.304134696

Solving
-13 + x = -13.304134696

Solving for variable 'x'.

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

Add '13' to each side of the equation.
-13 + 13 + x = -13.304134696 + 13

Combine like terms: -13 + 13 = 0
0 + x = -13.304134696 + 13
x = -13.304134696 + 13

Combine like terms: -13.304134696 + 13 = -0.304134696
x = -0.304134696

Simplifying
x = -0.304134696


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.304134696, -0.304134696}

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