2q^2+16q+22=0

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


Simplifying
2q2 + 16q + 22 = 0

Reorder the terms:
22 + 16q + 2q2 = 0

Solving
22 + 16q + 2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + 8q + q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11 + 8q + q2)' equal to zero and attempt to solve:

Simplifying
11 + 8q + q2 = 0

Solving
11 + 8q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 8q + -11 + q2 = 0 + -11

Reorder the terms:
11 + -11 + 8q + q2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 8q + q2 = 0 + -11
8q + q2 = 0 + -11

Combine like terms: 0 + -11 = -11
8q + q2 = -11

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

Add '16' to each side of the equation.
8q + 16 + q2 = -11 + 16

Reorder the terms:
16 + 8q + q2 = -11 + 16

Combine like terms: -11 + 16 = 5
16 + 8q + q2 = 5

Factor a perfect square on the left side:
(q + 4)(q + 4) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(q + 4) equal to 2.236067978 and -2.236067978.


Subproblem 1
q + 4 = 2.236067978

Simplifying
q + 4 = 2.236067978

Reorder the terms:
4 + q = 2.236067978

Solving
4 + q = 2.236067978

Solving for variable 'q'.

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

Add '-4' to each side of the equation.
4 + -4 + q = 2.236067978 + -4

Combine like terms: 4 + -4 = 0
0 + q = 2.236067978 + -4
q = 2.236067978 + -4

Combine like terms: 2.236067978 + -4 = -1.763932022
q = -1.763932022

Simplifying
q = -1.763932022


Subproblem 2
q + 4 = -2.236067978

Simplifying
q + 4 = -2.236067978

Reorder the terms:
4 + q = -2.236067978

Solving
4 + q = -2.236067978

Solving for variable 'q'.

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

Add '-4' to each side of the equation.
4 + -4 + q = -2.236067978 + -4

Combine like terms: 4 + -4 = 0
0 + q = -2.236067978 + -4
q = -2.236067978 + -4

Combine like terms: -2.236067978 + -4 = -6.236067978
q = -6.236067978

Simplifying
q = -6.236067978


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-1.763932022, -6.236067978}
Solution
q = {-1.763932022, -6.236067978}

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