0.9Q^2-3Q-14=0

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Solution for 0.9Q^2-3Q-14=0 equation: 


Simplifying
0.9Q2 + -3Q + -14 = 0

Reorder the terms:
-14 + -3Q + 0.9Q2 = 0

Solving
-14 + -3Q + 0.9Q2 = 0

Solving for variable 'Q'.

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

Divide each side by '0.9'.
-15.55555556 + -3.333333333Q + Q2 = 0

Move the constant term to the right:

Add '15.55555556' to each side of the equation.
-15.55555556 + -3.333333333Q + 15.55555556 + Q2 = 0 + 15.55555556

Reorder the terms:
-15.55555556 + 15.55555556 + -3.333333333Q + Q2 = 0 + 15.55555556

Combine like terms: -15.55555556 + 15.55555556 = 0.00000000
0.00000000 + -3.333333333Q + Q2 = 0 + 15.55555556
-3.333333333Q + Q2 = 0 + 15.55555556

Combine like terms: 0 + 15.55555556 = 15.55555556
-3.333333333Q + Q2 = 15.55555556

The Q term is -3.333333333Q.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333Q + 2.777777779 + Q2 = 15.55555556 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333Q + Q2 = 15.55555556 + 2.777777779

Combine like terms: 15.55555556 + 2.777777779 = 18.333333339
2.777777779 + -3.333333333Q + Q2 = 18.333333339

Factor a perfect square on the left side:
(Q + -1.666666667)(Q + -1.666666667) = 18.333333339

Calculate the square root of the right side: 4.281744194

Break this problem into two subproblems by setting 
(Q + -1.666666667) equal to 4.281744194 and -4.281744194.


Subproblem 1
Q + -1.666666667 = 4.281744194

Simplifying
Q + -1.666666667 = 4.281744194

Reorder the terms:
-1.666666667 + Q = 4.281744194

Solving
-1.666666667 + Q = 4.281744194

Solving for variable 'Q'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + Q = 4.281744194 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + Q = 4.281744194 + 1.666666667
Q = 4.281744194 + 1.666666667

Combine like terms: 4.281744194 + 1.666666667 = 5.948410861
Q = 5.948410861

Simplifying
Q = 5.948410861


Subproblem 2
Q + -1.666666667 = -4.281744194

Simplifying
Q + -1.666666667 = -4.281744194

Reorder the terms:
-1.666666667 + Q = -4.281744194

Solving
-1.666666667 + Q = -4.281744194

Solving for variable 'Q'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + Q = -4.281744194 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + Q = -4.281744194 + 1.666666667
Q = -4.281744194 + 1.666666667

Combine like terms: -4.281744194 + 1.666666667 = -2.615077527
Q = -2.615077527

Simplifying
Q = -2.615077527


Solution
The solution to the problem is based on the solutions
from the subproblems.
Q = {5.948410861, -2.615077527}

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