-3q^2+118.5q-328.5=0

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Solution for -3q^2+118.5q-328.5=0 equation:


Simplifying
-3q2 + 118.5q + -328.5 = 0

Reorder the terms:
-328.5 + 118.5q + -3q2 = 0

Solving
-328.5 + 118.5q + -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'.
109.5 + -39.5q + q2 = 0

Move the constant term to the right:

Add '-109.5' to each side of the equation.
109.5 + -39.5q + -109.5 + q2 = 0 + -109.5

Reorder the terms:
109.5 + -109.5 + -39.5q + q2 = 0 + -109.5

Combine like terms: 109.5 + -109.5 = 0.0
0.0 + -39.5q + q2 = 0 + -109.5
-39.5q + q2 = 0 + -109.5

Combine like terms: 0 + -109.5 = -109.5
-39.5q + q2 = -109.5

The q term is -39.5q.  Take half its coefficient (-19.75).
Square it (390.0625) and add it to both sides.

Add '390.0625' to each side of the equation.
-39.5q + 390.0625 + q2 = -109.5 + 390.0625

Reorder the terms:
390.0625 + -39.5q + q2 = -109.5 + 390.0625

Combine like terms: -109.5 + 390.0625 = 280.5625
390.0625 + -39.5q + q2 = 280.5625

Factor a perfect square on the left side:
(q + -19.75)(q + -19.75) = 280.5625

Calculate the square root of the right side: 16.75

Break this problem into two subproblems by setting 
(q + -19.75) equal to 16.75 and -16.75.

Subproblem 1

q + -19.75 = 16.75 Simplifying q + -19.75 = 16.75 Reorder the terms: -19.75 + q = 16.75 Solving -19.75 + q = 16.75 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '19.75' to each side of the equation. -19.75 + 19.75 + q = 16.75 + 19.75 Combine like terms: -19.75 + 19.75 = 0.00 0.00 + q = 16.75 + 19.75 q = 16.75 + 19.75 Combine like terms: 16.75 + 19.75 = 36.5 q = 36.5 Simplifying q = 36.5

Subproblem 2

q + -19.75 = -16.75 Simplifying q + -19.75 = -16.75 Reorder the terms: -19.75 + q = -16.75 Solving -19.75 + q = -16.75 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '19.75' to each side of the equation. -19.75 + 19.75 + q = -16.75 + 19.75 Combine like terms: -19.75 + 19.75 = 0.00 0.00 + q = -16.75 + 19.75 q = -16.75 + 19.75 Combine like terms: -16.75 + 19.75 = 3 q = 3 Simplifying q = 3

Solution

The solution to the problem is based on the solutions from the subproblems. q = {36.5, 3}

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