x^2-10x-125=0

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Solution for x^2-10x-125=0 equation: 


Simplifying
x2 + -10x + -125 = 0

Reorder the terms:
-125 + -10x + x2 = 0

Solving
-125 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + -10x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + -10x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + -10x + x2 = 0 + 125
-10x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
-10x + x2 = 125

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 125 + 25

Reorder the terms:
25 + -10x + x2 = 125 + 25

Combine like terms: 125 + 25 = 150
25 + -10x + x2 = 150

Factor a perfect square on the left side:
(x + -5)(x + -5) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(x + -5) equal to 12.247448714 and -12.247448714.


Subproblem 1
x + -5 = 12.247448714

Simplifying
x + -5 = 12.247448714

Reorder the terms:
-5 + x = 12.247448714

Solving
-5 + x = 12.247448714

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 12.247448714 + 5

Combine like terms: -5 + 5 = 0
0 + x = 12.247448714 + 5
x = 12.247448714 + 5

Combine like terms: 12.247448714 + 5 = 17.247448714
x = 17.247448714

Simplifying
x = 17.247448714


Subproblem 2
x + -5 = -12.247448714

Simplifying
x + -5 = -12.247448714

Reorder the terms:
-5 + x = -12.247448714

Solving
-5 + x = -12.247448714

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -12.247448714 + 5

Combine like terms: -5 + 5 = 0
0 + x = -12.247448714 + 5
x = -12.247448714 + 5

Combine like terms: -12.247448714 + 5 = -7.247448714
x = -7.247448714

Simplifying
x = -7.247448714


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.247448714, -7.247448714}

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