x^2-26x-133=0

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Solution for x^2-26x-133=0 equation: 


Simplifying
x2 + -26x + -133 = 0

Reorder the terms:
-133 + -26x + x2 = 0

Solving
-133 + -26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '133' to each side of the equation.
-133 + -26x + 133 + x2 = 0 + 133

Reorder the terms:
-133 + 133 + -26x + x2 = 0 + 133

Combine like terms: -133 + 133 = 0
0 + -26x + x2 = 0 + 133
-26x + x2 = 0 + 133

Combine like terms: 0 + 133 = 133
-26x + x2 = 133

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 = 133 + 169

Reorder the terms:
169 + -26x + x2 = 133 + 169

Combine like terms: 133 + 169 = 302
169 + -26x + x2 = 302

Factor a perfect square on the left side:
(x + -13)(x + -13) = 302

Calculate the square root of the right side: 17.378147197

Break this problem into two subproblems by setting 
(x + -13) equal to 17.378147197 and -17.378147197.


Subproblem 1
x + -13 = 17.378147197

Simplifying
x + -13 = 17.378147197

Reorder the terms:
-13 + x = 17.378147197

Solving
-13 + x = 17.378147197

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 = 17.378147197 + 13

Combine like terms: -13 + 13 = 0
0 + x = 17.378147197 + 13
x = 17.378147197 + 13

Combine like terms: 17.378147197 + 13 = 30.378147197
x = 30.378147197

Simplifying
x = 30.378147197


Subproblem 2
x + -13 = -17.378147197

Simplifying
x + -13 = -17.378147197

Reorder the terms:
-13 + x = -17.378147197

Solving
-13 + x = -17.378147197

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 = -17.378147197 + 13

Combine like terms: -13 + 13 = 0
0 + x = -17.378147197 + 13
x = -17.378147197 + 13

Combine like terms: -17.378147197 + 13 = -4.378147197
x = -4.378147197

Simplifying
x = -4.378147197


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.378147197, -4.378147197}

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