x^2-10x-107=0

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Solution for x^2-10x-107=0 equation: 


Simplifying
x2 + -10x + -107 = 0

Reorder the terms:
-107 + -10x + x2 = 0

Solving
-107 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '107' to each side of the equation.
-107 + -10x + 107 + x2 = 0 + 107

Reorder the terms:
-107 + 107 + -10x + x2 = 0 + 107

Combine like terms: -107 + 107 = 0
0 + -10x + x2 = 0 + 107
-10x + x2 = 0 + 107

Combine like terms: 0 + 107 = 107
-10x + x2 = 107

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 = 107 + 25

Reorder the terms:
25 + -10x + x2 = 107 + 25

Combine like terms: 107 + 25 = 132
25 + -10x + x2 = 132

Factor a perfect square on the left side:
(x + -5)(x + -5) = 132

Calculate the square root of the right side: 11.489125293

Break this problem into two subproblems by setting 
(x + -5) equal to 11.489125293 and -11.489125293.


Subproblem 1
x + -5 = 11.489125293

Simplifying
x + -5 = 11.489125293

Reorder the terms:
-5 + x = 11.489125293

Solving
-5 + x = 11.489125293

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 = 11.489125293 + 5

Combine like terms: -5 + 5 = 0
0 + x = 11.489125293 + 5
x = 11.489125293 + 5

Combine like terms: 11.489125293 + 5 = 16.489125293
x = 16.489125293

Simplifying
x = 16.489125293


Subproblem 2
x + -5 = -11.489125293

Simplifying
x + -5 = -11.489125293

Reorder the terms:
-5 + x = -11.489125293

Solving
-5 + x = -11.489125293

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 = -11.489125293 + 5

Combine like terms: -5 + 5 = 0
0 + x = -11.489125293 + 5
x = -11.489125293 + 5

Combine like terms: -11.489125293 + 5 = -6.489125293
x = -6.489125293

Simplifying
x = -6.489125293


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.489125293, -6.489125293}

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