3.25q^2+6q-76=

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Solution for 3.25q^2+6q-76= equation: 


Simplifying
3.25q2 + 6q + -76 = 0

Reorder the terms:
-76 + 6q + 3.25q2 = 0

Solving
-76 + 6q + 3.25q2 = 0

Solving for variable 'q'.

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

Divide each side by '3.25'.
-23.38461538 + 1.846153846q + q2 = 0

Move the constant term to the right:

Add '23.38461538' to each side of the equation.
-23.38461538 + 1.846153846q + 23.38461538 + q2 = 0 + 23.38461538

Reorder the terms:
-23.38461538 + 23.38461538 + 1.846153846q + q2 = 0 + 23.38461538

Combine like terms: -23.38461538 + 23.38461538 = 0.00000000
0.00000000 + 1.846153846q + q2 = 0 + 23.38461538
1.846153846q + q2 = 0 + 23.38461538

Combine like terms: 0 + 23.38461538 = 23.38461538
1.846153846q + q2 = 23.38461538

The q term is 1.846153846q.  Take half its coefficient (0.923076923).
Square it (0.8520710058) and add it to both sides.

Add '0.8520710058' to each side of the equation.
1.846153846q + 0.8520710058 + q2 = 23.38461538 + 0.8520710058

Reorder the terms:
0.8520710058 + 1.846153846q + q2 = 23.38461538 + 0.8520710058

Combine like terms: 23.38461538 + 0.8520710058 = 24.2366863858
0.8520710058 + 1.846153846q + q2 = 24.2366863858

Factor a perfect square on the left side:
(q + 0.923076923)(q + 0.923076923) = 24.2366863858

Calculate the square root of the right side: 4.923076923

Break this problem into two subproblems by setting 
(q + 0.923076923) equal to 4.923076923 and -4.923076923.


Subproblem 1
q + 0.923076923 = 4.923076923

Simplifying
q + 0.923076923 = 4.923076923

Reorder the terms:
0.923076923 + q = 4.923076923

Solving
0.923076923 + q = 4.923076923

Solving for variable 'q'.

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

Add '-0.923076923' to each side of the equation.
0.923076923 + -0.923076923 + q = 4.923076923 + -0.923076923

Combine like terms: 0.923076923 + -0.923076923 = 0.000000000
0.000000000 + q = 4.923076923 + -0.923076923
q = 4.923076923 + -0.923076923

Combine like terms: 4.923076923 + -0.923076923 = 4
q = 4

Simplifying
q = 4


Subproblem 2
q + 0.923076923 = -4.923076923

Simplifying
q + 0.923076923 = -4.923076923

Reorder the terms:
0.923076923 + q = -4.923076923

Solving
0.923076923 + q = -4.923076923

Solving for variable 'q'.

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

Add '-0.923076923' to each side of the equation.
0.923076923 + -0.923076923 + q = -4.923076923 + -0.923076923

Combine like terms: 0.923076923 + -0.923076923 = 0.000000000
0.000000000 + q = -4.923076923 + -0.923076923
q = -4.923076923 + -0.923076923

Combine like terms: -4.923076923 + -0.923076923 = -5.846153846
q = -5.846153846

Simplifying
q = -5.846153846


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {4, -5.846153846}

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