x^2-22x-15=0

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Solution for x^2-22x-15=0 equation: 


Simplifying
x2 + -22x + -15 = 0

Reorder the terms:
-15 + -22x + x2 = 0

Solving
-15 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -22x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -22x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -22x + x2 = 0 + 15
-22x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-22x + x2 = 15

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 = 15 + 121

Reorder the terms:
121 + -22x + x2 = 15 + 121

Combine like terms: 15 + 121 = 136
121 + -22x + x2 = 136

Factor a perfect square on the left side:
(x + -11)(x + -11) = 136

Calculate the square root of the right side: 11.66190379

Break this problem into two subproblems by setting 
(x + -11) equal to 11.66190379 and -11.66190379.


Subproblem 1
x + -11 = 11.66190379

Simplifying
x + -11 = 11.66190379

Reorder the terms:
-11 + x = 11.66190379

Solving
-11 + x = 11.66190379

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 = 11.66190379 + 11

Combine like terms: -11 + 11 = 0
0 + x = 11.66190379 + 11
x = 11.66190379 + 11

Combine like terms: 11.66190379 + 11 = 22.66190379
x = 22.66190379

Simplifying
x = 22.66190379


Subproblem 2
x + -11 = -11.66190379

Simplifying
x + -11 = -11.66190379

Reorder the terms:
-11 + x = -11.66190379

Solving
-11 + x = -11.66190379

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 = -11.66190379 + 11

Combine like terms: -11 + 11 = 0
0 + x = -11.66190379 + 11
x = -11.66190379 + 11

Combine like terms: -11.66190379 + 11 = -0.66190379
x = -0.66190379

Simplifying
x = -0.66190379


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.66190379, -0.66190379}

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