x^2-131x-144=0

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Solution for x^2-131x-144=0 equation: 


Simplifying
x2 + -131x + -144 = 0

Reorder the terms:
-144 + -131x + x2 = 0

Solving
-144 + -131x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + -131x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + -131x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + -131x + x2 = 0 + 144
-131x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
-131x + x2 = 144

The x term is -131x.  Take half its coefficient (-65.5).
Square it (4290.25) and add it to both sides.

Add '4290.25' to each side of the equation.
-131x + 4290.25 + x2 = 144 + 4290.25

Reorder the terms:
4290.25 + -131x + x2 = 144 + 4290.25

Combine like terms: 144 + 4290.25 = 4434.25
4290.25 + -131x + x2 = 4434.25

Factor a perfect square on the left side:
(x + -65.5)(x + -65.5) = 4434.25

Calculate the square root of the right side: 66.590164439

Break this problem into two subproblems by setting 
(x + -65.5) equal to 66.590164439 and -66.590164439.


Subproblem 1
x + -65.5 = 66.590164439

Simplifying
x + -65.5 = 66.590164439

Reorder the terms:
-65.5 + x = 66.590164439

Solving
-65.5 + x = 66.590164439

Solving for variable 'x'.

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

Add '65.5' to each side of the equation.
-65.5 + 65.5 + x = 66.590164439 + 65.5

Combine like terms: -65.5 + 65.5 = 0.0
0.0 + x = 66.590164439 + 65.5
x = 66.590164439 + 65.5

Combine like terms: 66.590164439 + 65.5 = 132.090164439
x = 132.090164439

Simplifying
x = 132.090164439


Subproblem 2
x + -65.5 = -66.590164439

Simplifying
x + -65.5 = -66.590164439

Reorder the terms:
-65.5 + x = -66.590164439

Solving
-65.5 + x = -66.590164439

Solving for variable 'x'.

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

Add '65.5' to each side of the equation.
-65.5 + 65.5 + x = -66.590164439 + 65.5

Combine like terms: -65.5 + 65.5 = 0.0
0.0 + x = -66.590164439 + 65.5
x = -66.590164439 + 65.5

Combine like terms: -66.590164439 + 65.5 = -1.090164439
x = -1.090164439

Simplifying
x = -1.090164439


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {132.090164439, -1.090164439}

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