x^2-10x-105=0

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Solution for x^2-10x-105=0 equation: 


Simplifying
x2 + -10x + -105 = 0

Reorder the terms:
-105 + -10x + x2 = 0

Solving
-105 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + -10x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + -10x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + -10x + x2 = 0 + 105
-10x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
-10x + x2 = 105

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 = 105 + 25

Reorder the terms:
25 + -10x + x2 = 105 + 25

Combine like terms: 105 + 25 = 130
25 + -10x + x2 = 130

Factor a perfect square on the left side:
(x + -5)(x + -5) = 130

Calculate the square root of the right side: 11.401754251

Break this problem into two subproblems by setting 
(x + -5) equal to 11.401754251 and -11.401754251.


Subproblem 1
x + -5 = 11.401754251

Simplifying
x + -5 = 11.401754251

Reorder the terms:
-5 + x = 11.401754251

Solving
-5 + x = 11.401754251

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 = 11.401754251 + 5

Combine like terms: -5 + 5 = 0
0 + x = 11.401754251 + 5
x = 11.401754251 + 5

Combine like terms: 11.401754251 + 5 = 16.401754251
x = 16.401754251

Simplifying
x = 16.401754251


Subproblem 2
x + -5 = -11.401754251

Simplifying
x + -5 = -11.401754251

Reorder the terms:
-5 + x = -11.401754251

Solving
-5 + x = -11.401754251

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 = -11.401754251 + 5

Combine like terms: -5 + 5 = 0
0 + x = -11.401754251 + 5
x = -11.401754251 + 5

Combine like terms: -11.401754251 + 5 = -6.401754251
x = -6.401754251

Simplifying
x = -6.401754251


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.401754251, -6.401754251}

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