x^2+8x=22

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Solution for x^2+8x=22 equation: 


Simplifying
x2 + 8x = 22

Reorder the terms:
8x + x2 = 22

Solving
8x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 8x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 8x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 8x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 8x + x2 = 0 + 22
8x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
8x + x2 = 22

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 22 + 16

Reorder the terms:
16 + 8x + x2 = 22 + 16

Combine like terms: 22 + 16 = 38
16 + 8x + x2 = 38

Factor a perfect square on the left side:
(x + 4)(x + 4) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(x + 4) equal to 6.164414003 and -6.164414003.


Subproblem 1
x + 4 = 6.164414003

Simplifying
x + 4 = 6.164414003

Reorder the terms:
4 + x = 6.164414003

Solving
4 + x = 6.164414003

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 6.164414003 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.164414003 + -4
x = 6.164414003 + -4

Combine like terms: 6.164414003 + -4 = 2.164414003
x = 2.164414003

Simplifying
x = 2.164414003


Subproblem 2
x + 4 = -6.164414003

Simplifying
x + 4 = -6.164414003

Reorder the terms:
4 + x = -6.164414003

Solving
4 + x = -6.164414003

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -6.164414003 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.164414003 + -4
x = -6.164414003 + -4

Combine like terms: -6.164414003 + -4 = -10.164414003
x = -10.164414003

Simplifying
x = -10.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.164414003, -10.164414003}

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