90=60+14Q+2Q^2

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Solution for 90=60+14Q+2Q^2 equation: 


Simplifying
90 = 60 + 14Q + 2Q2

Solving
90 = 60 + 14Q + 2Q2

Solving for variable 'Q'.

Combine like terms: 90 + -60 = 30
30 + -14Q + -2Q2 = 60 + 14Q + 2Q2 + -60 + -14Q + -2Q2

Reorder the terms:
30 + -14Q + -2Q2 = 60 + -60 + 14Q + -14Q + 2Q2 + -2Q2

Combine like terms: 60 + -60 = 0
30 + -14Q + -2Q2 = 0 + 14Q + -14Q + 2Q2 + -2Q2
30 + -14Q + -2Q2 = 14Q + -14Q + 2Q2 + -2Q2

Combine like terms: 14Q + -14Q = 0
30 + -14Q + -2Q2 = 0 + 2Q2 + -2Q2
30 + -14Q + -2Q2 = 2Q2 + -2Q2

Combine like terms: 2Q2 + -2Q2 = 0
30 + -14Q + -2Q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -7Q + -1Q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + -7Q + -1Q2)' equal to zero and attempt to solve:

Simplifying
15 + -7Q + -1Q2 = 0

Solving
15 + -7Q + -1Q2 = 0

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

Divide each side by '-1'.
-15 + 7Q + Q2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 7Q + 15 + Q2 = 0 + 15

Reorder the terms:
-15 + 15 + 7Q + Q2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 7Q + Q2 = 0 + 15
7Q + Q2 = 0 + 15

Combine like terms: 0 + 15 = 15
7Q + Q2 = 15

The Q term is 7Q.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7Q + 12.25 + Q2 = 15 + 12.25

Reorder the terms:
12.25 + 7Q + Q2 = 15 + 12.25

Combine like terms: 15 + 12.25 = 27.25
12.25 + 7Q + Q2 = 27.25

Factor a perfect square on the left side:
(Q + 3.5)(Q + 3.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(Q + 3.5) equal to 5.220153254 and -5.220153254.


Subproblem 1
Q + 3.5 = 5.220153254

Simplifying
Q + 3.5 = 5.220153254

Reorder the terms:
3.5 + Q = 5.220153254

Solving
3.5 + Q = 5.220153254

Solving for variable 'Q'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + Q = 5.220153254 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + Q = 5.220153254 + -3.5
Q = 5.220153254 + -3.5

Combine like terms: 5.220153254 + -3.5 = 1.720153254
Q = 1.720153254

Simplifying
Q = 1.720153254


Subproblem 2
Q + 3.5 = -5.220153254

Simplifying
Q + 3.5 = -5.220153254

Reorder the terms:
3.5 + Q = -5.220153254

Solving
3.5 + Q = -5.220153254

Solving for variable 'Q'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + Q = -5.220153254 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + Q = -5.220153254 + -3.5
Q = -5.220153254 + -3.5

Combine like terms: -5.220153254 + -3.5 = -8.720153254
Q = -8.720153254

Simplifying
Q = -8.720153254


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {1.720153254, -8.720153254}
Solution
Q = {1.720153254, -8.720153254}

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