=130+10Q+0.5Q^2

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Solution for =130+10Q+0.5Q^2 equation: 


Simplifying
0 = 130 + 10Q + 0.5Q2

Solving
0 = 130 + 10Q + 0.5Q2

Solving for variable 'Q'.

Combine like terms: 0 + -130 = -130
-130 + -10Q + -0.5Q2 = 130 + 10Q + 0.5Q2 + -130 + -10Q + -0.5Q2

Reorder the terms:
-130 + -10Q + -0.5Q2 = 130 + -130 + 10Q + -10Q + 0.5Q2 + -0.5Q2

Combine like terms: 130 + -130 = 0
-130 + -10Q + -0.5Q2 = 0 + 10Q + -10Q + 0.5Q2 + -0.5Q2
-130 + -10Q + -0.5Q2 = 10Q + -10Q + 0.5Q2 + -0.5Q2

Combine like terms: 10Q + -10Q = 0
-130 + -10Q + -0.5Q2 = 0 + 0.5Q2 + -0.5Q2
-130 + -10Q + -0.5Q2 = 0.5Q2 + -0.5Q2

Combine like terms: 0.5Q2 + -0.5Q2 = 0.0
-130 + -10Q + -0.5Q2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
260 + 20Q + Q2 = 0

Move the constant term to the right:

Add '-260' to each side of the equation.
260 + 20Q + -260 + Q2 = 0 + -260

Reorder the terms:
260 + -260 + 20Q + Q2 = 0 + -260

Combine like terms: 260 + -260 = 0
0 + 20Q + Q2 = 0 + -260
20Q + Q2 = 0 + -260

Combine like terms: 0 + -260 = -260
20Q + Q2 = -260

The Q term is 20Q.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20Q + 100 + Q2 = -260 + 100

Reorder the terms:
100 + 20Q + Q2 = -260 + 100

Combine like terms: -260 + 100 = -160
100 + 20Q + Q2 = -160

Factor a perfect square on the left side:
(Q + 10)(Q + 10) = -160

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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