3q^2+14q-156=0

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Solution for 3q^2+14q-156=0 equation: 


Simplifying
3q2 + 14q + -156 = 0

Reorder the terms:
-156 + 14q + 3q2 = 0

Solving
-156 + 14q + 3q2 = 0

Solving for variable 'q'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-52 + 4.666666667q + q2 = 0

Move the constant term to the right:

Add '52' to each side of the equation.
-52 + 4.666666667q + 52 + q2 = 0 + 52

Reorder the terms:
-52 + 52 + 4.666666667q + q2 = 0 + 52

Combine like terms: -52 + 52 = 0
0 + 4.666666667q + q2 = 0 + 52
4.666666667q + q2 = 0 + 52

Combine like terms: 0 + 52 = 52
4.666666667q + q2 = 52

The q term is 4.666666667q.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667q + 5.444444448 + q2 = 52 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667q + q2 = 52 + 5.444444448

Combine like terms: 52 + 5.444444448 = 57.444444448
5.444444448 + 4.666666667q + q2 = 57.444444448

Factor a perfect square on the left side:
(q + 2.333333334)(q + 2.333333334) = 57.444444448

Calculate the square root of the right side: 7.579211334

Break this problem into two subproblems by setting 
(q + 2.333333334) equal to 7.579211334 and -7.579211334.


Subproblem 1
q + 2.333333334 = 7.579211334

Simplifying
q + 2.333333334 = 7.579211334

Reorder the terms:
2.333333334 + q = 7.579211334

Solving
2.333333334 + q = 7.579211334

Solving for variable 'q'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + q = 7.579211334 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + q = 7.579211334 + -2.333333334
q = 7.579211334 + -2.333333334

Combine like terms: 7.579211334 + -2.333333334 = 5.245878
q = 5.245878

Simplifying
q = 5.245878


Subproblem 2
q + 2.333333334 = -7.579211334

Simplifying
q + 2.333333334 = -7.579211334

Reorder the terms:
2.333333334 + q = -7.579211334

Solving
2.333333334 + q = -7.579211334

Solving for variable 'q'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + q = -7.579211334 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + q = -7.579211334 + -2.333333334
q = -7.579211334 + -2.333333334

Combine like terms: -7.579211334 + -2.333333334 = -9.912544668
q = -9.912544668

Simplifying
q = -9.912544668


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {5.245878, -9.912544668}

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