0=x^2+22x-16

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Solution for 0=x^2+22x-16 equation: 


Simplifying
0 = x2 + 22x + -16

Reorder the terms:
0 = -16 + 22x + x2

Solving
0 = -16 + 22x + x2

Solving for variable 'x'.

Combine like terms: 0 + 16 = 16
16 + -22x + -1x2 = -16 + 22x + x2 + 16 + -22x + -1x2

Reorder the terms:
16 + -22x + -1x2 = -16 + 16 + 22x + -22x + x2 + -1x2

Combine like terms: -16 + 16 = 0
16 + -22x + -1x2 = 0 + 22x + -22x + x2 + -1x2
16 + -22x + -1x2 = 22x + -22x + x2 + -1x2

Combine like terms: 22x + -22x = 0
16 + -22x + -1x2 = 0 + x2 + -1x2
16 + -22x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -22x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + 22x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 22x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 22x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 22x + x2 = 0 + 16
22x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
22x + x2 = 16

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 = 16 + 121

Reorder the terms:
121 + 22x + x2 = 16 + 121

Combine like terms: 16 + 121 = 137
121 + 22x + x2 = 137

Factor a perfect square on the left side:
(x + 11)(x + 11) = 137

Calculate the square root of the right side: 11.704699911

Break this problem into two subproblems by setting 
(x + 11) equal to 11.704699911 and -11.704699911.


Subproblem 1
x + 11 = 11.704699911

Simplifying
x + 11 = 11.704699911

Reorder the terms:
11 + x = 11.704699911

Solving
11 + x = 11.704699911

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 = 11.704699911 + -11

Combine like terms: 11 + -11 = 0
0 + x = 11.704699911 + -11
x = 11.704699911 + -11

Combine like terms: 11.704699911 + -11 = 0.704699911
x = 0.704699911

Simplifying
x = 0.704699911


Subproblem 2
x + 11 = -11.704699911

Simplifying
x + 11 = -11.704699911

Reorder the terms:
11 + x = -11.704699911

Solving
11 + x = -11.704699911

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 = -11.704699911 + -11

Combine like terms: 11 + -11 = 0
0 + x = -11.704699911 + -11
x = -11.704699911 + -11

Combine like terms: -11.704699911 + -11 = -22.704699911
x = -22.704699911

Simplifying
x = -22.704699911


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.704699911, -22.704699911}

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