x^2+16x+22=0

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


Simplifying
x2 + 16x + 22 = 0

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

Solving
22 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -22 + 64

Reorder the terms:
64 + 16x + x2 = -22 + 64

Combine like terms: -22 + 64 = 42
64 + 16x + x2 = 42

Factor a perfect square on the left side:
(x + 8)(x + 8) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(x + 8) equal to 6.480740698 and -6.480740698.


Subproblem 1
x + 8 = 6.480740698

Simplifying
x + 8 = 6.480740698

Reorder the terms:
8 + x = 6.480740698

Solving
8 + x = 6.480740698

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 6.480740698 + -8

Combine like terms: 8 + -8 = 0
0 + x = 6.480740698 + -8
x = 6.480740698 + -8

Combine like terms: 6.480740698 + -8 = -1.519259302
x = -1.519259302

Simplifying
x = -1.519259302


Subproblem 2
x + 8 = -6.480740698

Simplifying
x + 8 = -6.480740698

Reorder the terms:
8 + x = -6.480740698

Solving
8 + x = -6.480740698

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -6.480740698 + -8

Combine like terms: 8 + -8 = 0
0 + x = -6.480740698 + -8
x = -6.480740698 + -8

Combine like terms: -6.480740698 + -8 = -14.480740698
x = -14.480740698

Simplifying
x = -14.480740698


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.519259302, -14.480740698}

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