12q^2-35q-8=0

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Solution for 12q^2-35q-8=0 equation: 


Simplifying
12q2 + -35q + -8 = 0

Reorder the terms:
-8 + -35q + 12q2 = 0

Solving
-8 + -35q + 12q2 = 0

Solving for variable 'q'.

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

Divide each side by '12'.
-0.6666666667 + -2.916666667q + q2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2.916666667q + 0.6666666667 + q2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2.916666667q + q2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2.916666667q + q2 = 0 + 0.6666666667
-2.916666667q + q2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2.916666667q + q2 = 0.6666666667

The q term is -2.916666667q.  Take half its coefficient (-1.458333334).
Square it (2.126736113) and add it to both sides.

Add '2.126736113' to each side of the equation.
-2.916666667q + 2.126736113 + q2 = 0.6666666667 + 2.126736113

Reorder the terms:
2.126736113 + -2.916666667q + q2 = 0.6666666667 + 2.126736113

Combine like terms: 0.6666666667 + 2.126736113 = 2.7934027797
2.126736113 + -2.916666667q + q2 = 2.7934027797

Factor a perfect square on the left side:
(q + -1.458333334)(q + -1.458333334) = 2.7934027797

Calculate the square root of the right side: 1.671347594

Break this problem into two subproblems by setting 
(q + -1.458333334) equal to 1.671347594 and -1.671347594.


Subproblem 1
q + -1.458333334 = 1.671347594

Simplifying
q + -1.458333334 = 1.671347594

Reorder the terms:
-1.458333334 + q = 1.671347594

Solving
-1.458333334 + q = 1.671347594

Solving for variable 'q'.

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

Add '1.458333334' to each side of the equation.
-1.458333334 + 1.458333334 + q = 1.671347594 + 1.458333334

Combine like terms: -1.458333334 + 1.458333334 = 0.000000000
0.000000000 + q = 1.671347594 + 1.458333334
q = 1.671347594 + 1.458333334

Combine like terms: 1.671347594 + 1.458333334 = 3.129680928
q = 3.129680928

Simplifying
q = 3.129680928


Subproblem 2
q + -1.458333334 = -1.671347594

Simplifying
q + -1.458333334 = -1.671347594

Reorder the terms:
-1.458333334 + q = -1.671347594

Solving
-1.458333334 + q = -1.671347594

Solving for variable 'q'.

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

Add '1.458333334' to each side of the equation.
-1.458333334 + 1.458333334 + q = -1.671347594 + 1.458333334

Combine like terms: -1.458333334 + 1.458333334 = 0.000000000
0.000000000 + q = -1.671347594 + 1.458333334
q = -1.671347594 + 1.458333334

Combine like terms: -1.671347594 + 1.458333334 = -0.21301426
q = -0.21301426

Simplifying
q = -0.21301426


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {3.129680928, -0.21301426}

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