-2q^2-60q-46=0

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Solution for -2q^2-60q-46=0 equation: 


Simplifying
-2q2 + -60q + -46 = 0

Reorder the terms:
-46 + -60q + -2q2 = 0

Solving
-46 + -60q + -2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(23 + 30q + q2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(23 + 30q + q2)' equal to zero and attempt to solve:

Simplifying
23 + 30q + q2 = 0

Solving
23 + 30q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 30q + -23 + q2 = 0 + -23

Reorder the terms:
23 + -23 + 30q + q2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 30q + q2 = 0 + -23
30q + q2 = 0 + -23

Combine like terms: 0 + -23 = -23
30q + q2 = -23

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 = -23 + 225

Reorder the terms:
225 + 30q + q2 = -23 + 225

Combine like terms: -23 + 225 = 202
225 + 30q + q2 = 202

Factor a perfect square on the left side:
(q + 15)(q + 15) = 202

Calculate the square root of the right side: 14.212670404

Break this problem into two subproblems by setting 
(q + 15) equal to 14.212670404 and -14.212670404.


Subproblem 1
q + 15 = 14.212670404

Simplifying
q + 15 = 14.212670404

Reorder the terms:
15 + q = 14.212670404

Solving
15 + q = 14.212670404

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 = 14.212670404 + -15

Combine like terms: 15 + -15 = 0
0 + q = 14.212670404 + -15
q = 14.212670404 + -15

Combine like terms: 14.212670404 + -15 = -0.787329596
q = -0.787329596

Simplifying
q = -0.787329596


Subproblem 2
q + 15 = -14.212670404

Simplifying
q + 15 = -14.212670404

Reorder the terms:
15 + q = -14.212670404

Solving
15 + q = -14.212670404

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 = -14.212670404 + -15

Combine like terms: 15 + -15 = 0
0 + q = -14.212670404 + -15
q = -14.212670404 + -15

Combine like terms: -14.212670404 + -15 = -29.212670404
q = -29.212670404

Simplifying
q = -29.212670404


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-0.787329596, -29.212670404}
Solution
q = {-0.787329596, -29.212670404}

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