-3q^2+440q-16=0

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Solution for -3q^2+440q-16=0 equation: 


Simplifying
-3q2 + 440q + -16 = 0

Reorder the terms:
-16 + 440q + -3q2 = 0

Solving
-16 + 440q + -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'.
5.333333333 + -146.6666667q + q2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -146.6666667q + -5.333333333 + q2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -146.6666667q + q2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -146.6666667q + q2 = 0 + -5.333333333
-146.6666667q + q2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-146.6666667q + q2 = -5.333333333

The q term is -146.6666667q.  Take half its coefficient (-73.33333335).
Square it (5377.777780) and add it to both sides.

Add '5377.777780' to each side of the equation.
-146.6666667q + 5377.777780 + q2 = -5.333333333 + 5377.777780

Reorder the terms:
5377.777780 + -146.6666667q + q2 = -5.333333333 + 5377.777780

Combine like terms: -5.333333333 + 5377.777780 = 5372.444446667
5377.777780 + -146.6666667q + q2 = 5372.444446667

Factor a perfect square on the left side:
(q + -73.33333335)(q + -73.33333335) = 5372.444446667

Calculate the square root of the right side: 73.296960692

Break this problem into two subproblems by setting 
(q + -73.33333335) equal to 73.296960692 and -73.296960692.


Subproblem 1
q + -73.33333335 = 73.296960692

Simplifying
q + -73.33333335 = 73.296960692

Reorder the terms:
-73.33333335 + q = 73.296960692

Solving
-73.33333335 + q = 73.296960692

Solving for variable 'q'.

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

Add '73.33333335' to each side of the equation.
-73.33333335 + 73.33333335 + q = 73.296960692 + 73.33333335

Combine like terms: -73.33333335 + 73.33333335 = 0.00000000
0.00000000 + q = 73.296960692 + 73.33333335
q = 73.296960692 + 73.33333335

Combine like terms: 73.296960692 + 73.33333335 = 146.630294042
q = 146.630294042

Simplifying
q = 146.630294042


Subproblem 2
q + -73.33333335 = -73.296960692

Simplifying
q + -73.33333335 = -73.296960692

Reorder the terms:
-73.33333335 + q = -73.296960692

Solving
-73.33333335 + q = -73.296960692

Solving for variable 'q'.

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

Add '73.33333335' to each side of the equation.
-73.33333335 + 73.33333335 + q = -73.296960692 + 73.33333335

Combine like terms: -73.33333335 + 73.33333335 = 0.00000000
0.00000000 + q = -73.296960692 + 73.33333335
q = -73.296960692 + 73.33333335

Combine like terms: -73.296960692 + 73.33333335 = 0.036372658
q = 0.036372658

Simplifying
q = 0.036372658


Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {146.630294042, 0.036372658}

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