3Q^2-34Q+24=0

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Solution for 3Q^2-34Q+24=0 equation: 


Simplifying
3Q2 + -34Q + 24 = 0

Reorder the terms:
24 + -34Q + 3Q2 = 0

Solving
24 + -34Q + 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'.
8 + -11.33333333Q + Q2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -11.33333333Q + -8 + Q2 = 0 + -8

Reorder the terms:
8 + -8 + -11.33333333Q + Q2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -11.33333333Q + Q2 = 0 + -8
-11.33333333Q + Q2 = 0 + -8

Combine like terms: 0 + -8 = -8
-11.33333333Q + Q2 = -8

The Q term is -11.33333333Q.  Take half its coefficient (-5.666666665).
Square it (32.11111109) and add it to both sides.

Add '32.11111109' to each side of the equation.
-11.33333333Q + 32.11111109 + Q2 = -8 + 32.11111109

Reorder the terms:
32.11111109 + -11.33333333Q + Q2 = -8 + 32.11111109

Combine like terms: -8 + 32.11111109 = 24.11111109
32.11111109 + -11.33333333Q + Q2 = 24.11111109

Factor a perfect square on the left side:
(Q + -5.666666665)(Q + -5.666666665) = 24.11111109

Calculate the square root of the right side: 4.910306619

Break this problem into two subproblems by setting 
(Q + -5.666666665) equal to 4.910306619 and -4.910306619.


Subproblem 1
Q + -5.666666665 = 4.910306619

Simplifying
Q + -5.666666665 = 4.910306619

Reorder the terms:
-5.666666665 + Q = 4.910306619

Solving
-5.666666665 + Q = 4.910306619

Solving for variable 'Q'.

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

Add '5.666666665' to each side of the equation.
-5.666666665 + 5.666666665 + Q = 4.910306619 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + Q = 4.910306619 + 5.666666665
Q = 4.910306619 + 5.666666665

Combine like terms: 4.910306619 + 5.666666665 = 10.576973284
Q = 10.576973284

Simplifying
Q = 10.576973284


Subproblem 2
Q + -5.666666665 = -4.910306619

Simplifying
Q + -5.666666665 = -4.910306619

Reorder the terms:
-5.666666665 + Q = -4.910306619

Solving
-5.666666665 + Q = -4.910306619

Solving for variable 'Q'.

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

Add '5.666666665' to each side of the equation.
-5.666666665 + 5.666666665 + Q = -4.910306619 + 5.666666665

Combine like terms: -5.666666665 + 5.666666665 = 0.000000000
0.000000000 + Q = -4.910306619 + 5.666666665
Q = -4.910306619 + 5.666666665

Combine like terms: -4.910306619 + 5.666666665 = 0.756360046
Q = 0.756360046

Simplifying
Q = 0.756360046


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {10.576973284, 0.756360046}

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