50=1000+2Q+.25Q^2

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Solution for 50=1000+2Q+.25Q^2 equation: 


Simplifying
50 = 1000 + 2Q + 0.25Q2

Solving
50 = 1000 + 2Q + 0.25Q2

Solving for variable 'Q'.

Combine like terms: 50 + -1000 = -950
-950 + -2Q + -0.25Q2 = 1000 + 2Q + 0.25Q2 + -1000 + -2Q + -0.25Q2

Reorder the terms:
-950 + -2Q + -0.25Q2 = 1000 + -1000 + 2Q + -2Q + 0.25Q2 + -0.25Q2

Combine like terms: 1000 + -1000 = 0
-950 + -2Q + -0.25Q2 = 0 + 2Q + -2Q + 0.25Q2 + -0.25Q2
-950 + -2Q + -0.25Q2 = 2Q + -2Q + 0.25Q2 + -0.25Q2

Combine like terms: 2Q + -2Q = 0
-950 + -2Q + -0.25Q2 = 0 + 0.25Q2 + -0.25Q2
-950 + -2Q + -0.25Q2 = 0.25Q2 + -0.25Q2

Combine like terms: 0.25Q2 + -0.25Q2 = 0.00
-950 + -2Q + -0.25Q2 = 0.00

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
3800 + 8Q + Q2 = 0

Move the constant term to the right:

Add '-3800' to each side of the equation.
3800 + 8Q + -3800 + Q2 = 0 + -3800

Reorder the terms:
3800 + -3800 + 8Q + Q2 = 0 + -3800

Combine like terms: 3800 + -3800 = 0
0 + 8Q + Q2 = 0 + -3800
8Q + Q2 = 0 + -3800

Combine like terms: 0 + -3800 = -3800
8Q + Q2 = -3800

The Q term is 8Q.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8Q + 16 + Q2 = -3800 + 16

Reorder the terms:
16 + 8Q + Q2 = -3800 + 16

Combine like terms: -3800 + 16 = -3784
16 + 8Q + Q2 = -3784

Factor a perfect square on the left side:
(Q + 4)(Q + 4) = -3784

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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