x^2-6x-56=10

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Solution for x^2-6x-56=10 equation: 


Simplifying
x2 + -6x + -56 = 10

Reorder the terms:
-56 + -6x + x2 = 10

Solving
-56 + -6x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-56 + -10 + -6x + x2 = 10 + -10

Combine like terms: -56 + -10 = -66
-66 + -6x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-66 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + -6x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + -6x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + -6x + x2 = 0 + 66
-6x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
-6x + x2 = 66

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 66 + 9

Reorder the terms:
9 + -6x + x2 = 66 + 9

Combine like terms: 66 + 9 = 75
9 + -6x + x2 = 75

Factor a perfect square on the left side:
(x + -3)(x + -3) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -3) equal to 8.660254038 and -8.660254038.


Subproblem 1
x + -3 = 8.660254038

Simplifying
x + -3 = 8.660254038

Reorder the terms:
-3 + x = 8.660254038

Solving
-3 + x = 8.660254038

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 8.660254038 + 3

Combine like terms: -3 + 3 = 0
0 + x = 8.660254038 + 3
x = 8.660254038 + 3

Combine like terms: 8.660254038 + 3 = 11.660254038
x = 11.660254038

Simplifying
x = 11.660254038


Subproblem 2
x + -3 = -8.660254038

Simplifying
x + -3 = -8.660254038

Reorder the terms:
-3 + x = -8.660254038

Solving
-3 + x = -8.660254038

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -8.660254038 + 3

Combine like terms: -3 + 3 = 0
0 + x = -8.660254038 + 3
x = -8.660254038 + 3

Combine like terms: -8.660254038 + 3 = -5.660254038
x = -5.660254038

Simplifying
x = -5.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.660254038, -5.660254038}

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