x^2+22x-100=0

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Solution for x^2+22x-100=0 equation: 


Simplifying
x2 + 22x + -100 = 0

Reorder the terms:
-100 + 22x + x2 = 0

Solving
-100 + 22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 22x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 22x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 22x + x2 = 0 + 100
22x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
22x + x2 = 100

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 = 100 + 121

Reorder the terms:
121 + 22x + x2 = 100 + 121

Combine like terms: 100 + 121 = 221
121 + 22x + x2 = 221

Factor a perfect square on the left side:
(x + 11)(x + 11) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(x + 11) equal to 14.866068747 and -14.866068747.


Subproblem 1
x + 11 = 14.866068747

Simplifying
x + 11 = 14.866068747

Reorder the terms:
11 + x = 14.866068747

Solving
11 + x = 14.866068747

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 = 14.866068747 + -11

Combine like terms: 11 + -11 = 0
0 + x = 14.866068747 + -11
x = 14.866068747 + -11

Combine like terms: 14.866068747 + -11 = 3.866068747
x = 3.866068747

Simplifying
x = 3.866068747


Subproblem 2
x + 11 = -14.866068747

Simplifying
x + 11 = -14.866068747

Reorder the terms:
11 + x = -14.866068747

Solving
11 + x = -14.866068747

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 = -14.866068747 + -11

Combine like terms: 11 + -11 = 0
0 + x = -14.866068747 + -11
x = -14.866068747 + -11

Combine like terms: -14.866068747 + -11 = -25.866068747
x = -25.866068747

Simplifying
x = -25.866068747


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.866068747, -25.866068747}

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