x^2-5x-130=0

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Solution for x^2-5x-130=0 equation: 


Simplifying
x2 + -5x + -130 = 0

Reorder the terms:
-130 + -5x + x2 = 0

Solving
-130 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + -5x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + -5x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + -5x + x2 = 0 + 130
-5x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
-5x + x2 = 130

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 130 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 130 + 6.25

Combine like terms: 130 + 6.25 = 136.25
6.25 + -5x + x2 = 136.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 136.25

Calculate the square root of the right side: 11.67261753

Break this problem into two subproblems by setting 
(x + -2.5) equal to 11.67261753 and -11.67261753.


Subproblem 1
x + -2.5 = 11.67261753

Simplifying
x + -2.5 = 11.67261753

Reorder the terms:
-2.5 + x = 11.67261753

Solving
-2.5 + x = 11.67261753

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 11.67261753 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 11.67261753 + 2.5
x = 11.67261753 + 2.5

Combine like terms: 11.67261753 + 2.5 = 14.17261753
x = 14.17261753

Simplifying
x = 14.17261753


Subproblem 2
x + -2.5 = -11.67261753

Simplifying
x + -2.5 = -11.67261753

Reorder the terms:
-2.5 + x = -11.67261753

Solving
-2.5 + x = -11.67261753

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -11.67261753 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -11.67261753 + 2.5
x = -11.67261753 + 2.5

Combine like terms: -11.67261753 + 2.5 = -9.17261753
x = -9.17261753

Simplifying
x = -9.17261753


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.17261753, -9.17261753}

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