2q^2+22q-60=0

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Solution for 2q^2+22q-60=0 equation: 


Simplifying
2q2 + 22q + -60 = 0

Reorder the terms:
-60 + 22q + 2q2 = 0

Solving
-60 + 22q + 2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 11q + q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + 11q + q2)' equal to zero and attempt to solve:

Simplifying
-30 + 11q + q2 = 0

Solving
-30 + 11q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 11q + 30 + q2 = 0 + 30

Reorder the terms:
-30 + 30 + 11q + q2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 11q + q2 = 0 + 30
11q + q2 = 0 + 30

Combine like terms: 0 + 30 = 30
11q + q2 = 30

The q term is 11q.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11q + 30.25 + q2 = 30 + 30.25

Reorder the terms:
30.25 + 11q + q2 = 30 + 30.25

Combine like terms: 30 + 30.25 = 60.25
30.25 + 11q + q2 = 60.25

Factor a perfect square on the left side:
(q + 5.5)(q + 5.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(q + 5.5) equal to 7.762087348 and -7.762087348.


Subproblem 1
q + 5.5 = 7.762087348

Simplifying
q + 5.5 = 7.762087348

Reorder the terms:
5.5 + q = 7.762087348

Solving
5.5 + q = 7.762087348

Solving for variable 'q'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + q = 7.762087348 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + q = 7.762087348 + -5.5
q = 7.762087348 + -5.5

Combine like terms: 7.762087348 + -5.5 = 2.262087348
q = 2.262087348

Simplifying
q = 2.262087348


Subproblem 2
q + 5.5 = -7.762087348

Simplifying
q + 5.5 = -7.762087348

Reorder the terms:
5.5 + q = -7.762087348

Solving
5.5 + q = -7.762087348

Solving for variable 'q'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + q = -7.762087348 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + q = -7.762087348 + -5.5
q = -7.762087348 + -5.5

Combine like terms: -7.762087348 + -5.5 = -13.262087348
q = -13.262087348

Simplifying
q = -13.262087348


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {2.262087348, -13.262087348}
Solution
q = {2.262087348, -13.262087348}

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