-(Q^2)+24Q-40=0

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Solution for -(Q^2)+24Q-40=0 equation: 


Simplifying
-1(Q2) + 24Q + -40 = 0

Reorder the terms:
-40 + 24Q + -1Q2 = 0

Solving
-40 + 24Q + -1Q2 = 0

Solving for variable 'Q'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
40 + -24Q + Q2 = 0

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -24Q + -40 + Q2 = 0 + -40

Reorder the terms:
40 + -40 + -24Q + Q2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -24Q + Q2 = 0 + -40
-24Q + Q2 = 0 + -40

Combine like terms: 0 + -40 = -40
-24Q + Q2 = -40

The Q term is -24Q.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24Q + 144 + Q2 = -40 + 144

Reorder the terms:
144 + -24Q + Q2 = -40 + 144

Combine like terms: -40 + 144 = 104
144 + -24Q + Q2 = 104

Factor a perfect square on the left side:
(Q + -12)(Q + -12) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(Q + -12) equal to 10.198039027 and -10.198039027.


Subproblem 1
Q + -12 = 10.198039027

Simplifying
Q + -12 = 10.198039027

Reorder the terms:
-12 + Q = 10.198039027

Solving
-12 + Q = 10.198039027

Solving for variable 'Q'.

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

Add '12' to each side of the equation.
-12 + 12 + Q = 10.198039027 + 12

Combine like terms: -12 + 12 = 0
0 + Q = 10.198039027 + 12
Q = 10.198039027 + 12

Combine like terms: 10.198039027 + 12 = 22.198039027
Q = 22.198039027

Simplifying
Q = 22.198039027


Subproblem 2
Q + -12 = -10.198039027

Simplifying
Q + -12 = -10.198039027

Reorder the terms:
-12 + Q = -10.198039027

Solving
-12 + Q = -10.198039027

Solving for variable 'Q'.

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

Add '12' to each side of the equation.
-12 + 12 + Q = -10.198039027 + 12

Combine like terms: -12 + 12 = 0
0 + Q = -10.198039027 + 12
Q = -10.198039027 + 12

Combine like terms: -10.198039027 + 12 = 1.801960973
Q = 1.801960973

Simplifying
Q = 1.801960973


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {22.198039027, 1.801960973}

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