2q^2+60q-2=0

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


Simplifying
2q2 + 60q + -2 = 0

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

Solving
-2 + 60q + 2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 30q + q2) = 0

Ignore the factor 2.

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

Simplifying
-1 + 30q + q2 = 0

Solving
-1 + 30q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 30q + 1 + q2 = 0 + 1

Reorder the terms:
-1 + 1 + 30q + q2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 30q + q2 = 0 + 1
30q + q2 = 0 + 1

Combine like terms: 0 + 1 = 1
30q + q2 = 1

The q term is 30q.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30q + 225 + q2 = 1 + 225

Reorder the terms:
225 + 30q + q2 = 1 + 225

Combine like terms: 1 + 225 = 226
225 + 30q + q2 = 226

Factor a perfect square on the left side:
(q + 15)(q + 15) = 226

Calculate the square root of the right side: 15.033296378

Break this problem into two subproblems by setting 
(q + 15) equal to 15.033296378 and -15.033296378.


Subproblem 1
q + 15 = 15.033296378

Simplifying
q + 15 = 15.033296378

Reorder the terms:
15 + q = 15.033296378

Solving
15 + q = 15.033296378

Solving for variable 'q'.

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

Add '-15' to each side of the equation.
15 + -15 + q = 15.033296378 + -15

Combine like terms: 15 + -15 = 0
0 + q = 15.033296378 + -15
q = 15.033296378 + -15

Combine like terms: 15.033296378 + -15 = 0.033296378
q = 0.033296378

Simplifying
q = 0.033296378


Subproblem 2
q + 15 = -15.033296378

Simplifying
q + 15 = -15.033296378

Reorder the terms:
15 + q = -15.033296378

Solving
15 + q = -15.033296378

Solving for variable 'q'.

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

Add '-15' to each side of the equation.
15 + -15 + q = -15.033296378 + -15

Combine like terms: 15 + -15 = 0
0 + q = -15.033296378 + -15
q = -15.033296378 + -15

Combine like terms: -15.033296378 + -15 = -30.033296378
q = -30.033296378

Simplifying
q = -30.033296378


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {0.033296378, -30.033296378}
Solution
q = {0.033296378, -30.033296378}

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