0=Q^2+60Q+1000

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Solution for 0=Q^2+60Q+1000 equation: 


Simplifying
0 = Q2 + 60Q + 1000

Reorder the terms:
0 = 1000 + 60Q + Q2

Solving
0 = 1000 + 60Q + Q2

Solving for variable 'Q'.

Combine like terms: 0 + -1000 = -1000
-1000 + -60Q + -1Q2 = 1000 + 60Q + Q2 + -1000 + -60Q + -1Q2

Reorder the terms:
-1000 + -60Q + -1Q2 = 1000 + -1000 + 60Q + -60Q + Q2 + -1Q2

Combine like terms: 1000 + -1000 = 0
-1000 + -60Q + -1Q2 = 0 + 60Q + -60Q + Q2 + -1Q2
-1000 + -60Q + -1Q2 = 60Q + -60Q + Q2 + -1Q2

Combine like terms: 60Q + -60Q = 0
-1000 + -60Q + -1Q2 = 0 + Q2 + -1Q2
-1000 + -60Q + -1Q2 = Q2 + -1Q2

Combine like terms: Q2 + -1Q2 = 0
-1000 + -60Q + -1Q2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1000 + 60Q + Q2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1000 + 60Q + Q2)' equal to zero and attempt to solve:

Simplifying
1000 + 60Q + Q2 = 0

Solving
1000 + 60Q + Q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + 60Q + -1000 + Q2 = 0 + -1000

Reorder the terms:
1000 + -1000 + 60Q + Q2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + 60Q + Q2 = 0 + -1000
60Q + Q2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
60Q + Q2 = -1000

The Q term is 60Q.  Take half its coefficient (30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
60Q + 900 + Q2 = -1000 + 900

Reorder the terms:
900 + 60Q + Q2 = -1000 + 900

Combine like terms: -1000 + 900 = -100
900 + 60Q + Q2 = -100

Factor a perfect square on the left side:
(Q + 30)(Q + 30) = -100

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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