x^2-10x-1=13

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Solution for x^2-10x-1=13 equation: 


Simplifying
x2 + -10x + -1 = 13

Reorder the terms:
-1 + -10x + x2 = 13

Solving
-1 + -10x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
-1 + -13 + -10x + x2 = 13 + -13

Combine like terms: -1 + -13 = -14
-14 + -10x + x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-14 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -10x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -10x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -10x + x2 = 0 + 14
-10x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-10x + x2 = 14

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 = 14 + 25

Reorder the terms:
25 + -10x + x2 = 14 + 25

Combine like terms: 14 + 25 = 39
25 + -10x + x2 = 39

Factor a perfect square on the left side:
(x + -5)(x + -5) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + -5) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + -5 = 6.244997998

Simplifying
x + -5 = 6.244997998

Reorder the terms:
-5 + x = 6.244997998

Solving
-5 + x = 6.244997998

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 = 6.244997998 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.244997998 + 5
x = 6.244997998 + 5

Combine like terms: 6.244997998 + 5 = 11.244997998
x = 11.244997998

Simplifying
x = 11.244997998


Subproblem 2
x + -5 = -6.244997998

Simplifying
x + -5 = -6.244997998

Reorder the terms:
-5 + x = -6.244997998

Solving
-5 + x = -6.244997998

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 = -6.244997998 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.244997998 + 5
x = -6.244997998 + 5

Combine like terms: -6.244997998 + 5 = -1.244997998
x = -1.244997998

Simplifying
x = -1.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.244997998, -1.244997998}

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