300-6Q=1500+2Q^2

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Solution for 300-6Q=1500+2Q^2 equation: 


Simplifying
300 + -6Q = 1500 + 2Q2

Solving
300 + -6Q = 1500 + 2Q2

Solving for variable 'Q'.

Reorder the terms:
300 + -1500 + -6Q + -2Q2 = 1500 + 2Q2 + -1500 + -2Q2

Combine like terms: 300 + -1500 = -1200
-1200 + -6Q + -2Q2 = 1500 + 2Q2 + -1500 + -2Q2

Reorder the terms:
-1200 + -6Q + -2Q2 = 1500 + -1500 + 2Q2 + -2Q2

Combine like terms: 1500 + -1500 = 0
-1200 + -6Q + -2Q2 = 0 + 2Q2 + -2Q2
-1200 + -6Q + -2Q2 = 2Q2 + -2Q2

Combine like terms: 2Q2 + -2Q2 = 0
-1200 + -6Q + -2Q2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(600 + 3Q + Q2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(600 + 3Q + Q2)' equal to zero and attempt to solve:

Simplifying
600 + 3Q + Q2 = 0

Solving
600 + 3Q + Q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + 3Q + -600 + Q2 = 0 + -600

Reorder the terms:
600 + -600 + 3Q + Q2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + 3Q + Q2 = 0 + -600
3Q + Q2 = 0 + -600

Combine like terms: 0 + -600 = -600
3Q + Q2 = -600

The Q term is 3Q.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3Q + 2.25 + Q2 = -600 + 2.25

Reorder the terms:
2.25 + 3Q + Q2 = -600 + 2.25

Combine like terms: -600 + 2.25 = -597.75
2.25 + 3Q + Q2 = -597.75

Factor a perfect square on the left side:
(Q + 1.5)(Q + 1.5) = -597.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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