x^2-10x-6=11

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Solution for x^2-10x-6=11 equation: 


Simplifying
x2 + -10x + -6 = 11

Reorder the terms:
-6 + -10x + x2 = 11

Solving
-6 + -10x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
-6 + -11 + -10x + x2 = 11 + -11

Combine like terms: -6 + -11 = -17
-17 + -10x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-17 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -10x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -10x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -10x + x2 = 0 + 17
-10x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-10x + x2 = 17

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 = 17 + 25

Reorder the terms:
25 + -10x + x2 = 17 + 25

Combine like terms: 17 + 25 = 42
25 + -10x + x2 = 42

Factor a perfect square on the left side:
(x + -5)(x + -5) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(x + -5) equal to 6.480740698 and -6.480740698.


Subproblem 1
x + -5 = 6.480740698

Simplifying
x + -5 = 6.480740698

Reorder the terms:
-5 + x = 6.480740698

Solving
-5 + x = 6.480740698

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 = 6.480740698 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.480740698 + 5
x = 6.480740698 + 5

Combine like terms: 6.480740698 + 5 = 11.480740698
x = 11.480740698

Simplifying
x = 11.480740698


Subproblem 2
x + -5 = -6.480740698

Simplifying
x + -5 = -6.480740698

Reorder the terms:
-5 + x = -6.480740698

Solving
-5 + x = -6.480740698

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 = -6.480740698 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.480740698 + 5
x = -6.480740698 + 5

Combine like terms: -6.480740698 + 5 = -1.480740698
x = -1.480740698

Simplifying
x = -1.480740698


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.480740698, -1.480740698}

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