110=60+14Q+2Q^2

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Solution for 110=60+14Q+2Q^2 equation: 


Simplifying
110 = 60 + 14Q + 2Q2

Solving
110 = 60 + 14Q + 2Q2

Solving for variable 'Q'.

Combine like terms: 110 + -60 = 50
50 + -14Q + -2Q2 = 60 + 14Q + 2Q2 + -60 + -14Q + -2Q2

Reorder the terms:
50 + -14Q + -2Q2 = 60 + -60 + 14Q + -14Q + 2Q2 + -2Q2

Combine like terms: 60 + -60 = 0
50 + -14Q + -2Q2 = 0 + 14Q + -14Q + 2Q2 + -2Q2
50 + -14Q + -2Q2 = 14Q + -14Q + 2Q2 + -2Q2

Combine like terms: 14Q + -14Q = 0
50 + -14Q + -2Q2 = 0 + 2Q2 + -2Q2
50 + -14Q + -2Q2 = 2Q2 + -2Q2

Combine like terms: 2Q2 + -2Q2 = 0
50 + -14Q + -2Q2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -7Q + -1Q2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + -7Q + -1Q2)' equal to zero and attempt to solve:

Simplifying
25 + -7Q + -1Q2 = 0

Solving
25 + -7Q + -1Q2 = 0

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

Divide each side by '-1'.
-25 + 7Q + Q2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 7Q + 25 + Q2 = 0 + 25

Reorder the terms:
-25 + 25 + 7Q + Q2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 7Q + Q2 = 0 + 25
7Q + Q2 = 0 + 25

Combine like terms: 0 + 25 = 25
7Q + Q2 = 25

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 = 25 + 12.25

Reorder the terms:
12.25 + 7Q + Q2 = 25 + 12.25

Combine like terms: 25 + 12.25 = 37.25
12.25 + 7Q + Q2 = 37.25

Factor a perfect square on the left side:
(Q + 3.5)(Q + 3.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(Q + 3.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
Q + 3.5 = 6.103277808

Simplifying
Q + 3.5 = 6.103277808

Reorder the terms:
3.5 + Q = 6.103277808

Solving
3.5 + Q = 6.103277808

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 = 6.103277808 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + Q = 6.103277808 + -3.5
Q = 6.103277808 + -3.5

Combine like terms: 6.103277808 + -3.5 = 2.603277808
Q = 2.603277808

Simplifying
Q = 2.603277808


Subproblem 2
Q + 3.5 = -6.103277808

Simplifying
Q + 3.5 = -6.103277808

Reorder the terms:
3.5 + Q = -6.103277808

Solving
3.5 + Q = -6.103277808

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 = -6.103277808 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + Q = -6.103277808 + -3.5
Q = -6.103277808 + -3.5

Combine like terms: -6.103277808 + -3.5 = -9.603277808
Q = -9.603277808

Simplifying
Q = -9.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {2.603277808, -9.603277808}
Solution
Q = {2.603277808, -9.603277808}

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