x^2-22x-56=0

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Solution for x^2-22x-56=0 equation: 


Simplifying
x2 + -22x + -56 = 0

Reorder the terms:
-56 + -22x + x2 = 0

Solving
-56 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + -22x + 56 + x2 = 0 + 56

Reorder the terms:
-56 + 56 + -22x + x2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + -22x + x2 = 0 + 56
-22x + x2 = 0 + 56

Combine like terms: 0 + 56 = 56
-22x + x2 = 56

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 56 + 121

Reorder the terms:
121 + -22x + x2 = 56 + 121

Combine like terms: 56 + 121 = 177
121 + -22x + x2 = 177

Factor a perfect square on the left side:
(x + -11)(x + -11) = 177

Calculate the square root of the right side: 13.304134696

Break this problem into two subproblems by setting 
(x + -11) equal to 13.304134696 and -13.304134696.


Subproblem 1
x + -11 = 13.304134696

Simplifying
x + -11 = 13.304134696

Reorder the terms:
-11 + x = 13.304134696

Solving
-11 + x = 13.304134696

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 13.304134696 + 11

Combine like terms: -11 + 11 = 0
0 + x = 13.304134696 + 11
x = 13.304134696 + 11

Combine like terms: 13.304134696 + 11 = 24.304134696
x = 24.304134696

Simplifying
x = 24.304134696


Subproblem 2
x + -11 = -13.304134696

Simplifying
x + -11 = -13.304134696

Reorder the terms:
-11 + x = -13.304134696

Solving
-11 + x = -13.304134696

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -13.304134696 + 11

Combine like terms: -11 + 11 = 0
0 + x = -13.304134696 + 11
x = -13.304134696 + 11

Combine like terms: -13.304134696 + 11 = -2.304134696
x = -2.304134696

Simplifying
x = -2.304134696


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.304134696, -2.304134696}

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