100=60Q+Q^2

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Solution for 100=60Q+Q^2 equation:


Simplifying
100 = 60Q + Q2

Solving
100 = 60Q + Q2

Solving for variable 'Q'.

Reorder the terms:
100 + -60Q + -1Q2 = 60Q + -60Q + Q2 + -1Q2

Combine like terms: 60Q + -60Q = 0
100 + -60Q + -1Q2 = 0 + Q2 + -1Q2
100 + -60Q + -1Q2 = Q2 + -1Q2

Combine like terms: Q2 + -1Q2 = 0
100 + -60Q + -1Q2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-100 + 60Q + Q2 = 0

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 60Q + 100 + Q2 = 0 + 100

Reorder the terms:
-100 + 100 + 60Q + Q2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 60Q + Q2 = 0 + 100
60Q + Q2 = 0 + 100

Combine like terms: 0 + 100 = 100
60Q + Q2 = 100

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 = 100 + 900

Reorder the terms:
900 + 60Q + Q2 = 100 + 900

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

Factor a perfect square on the left side:
(Q + 30)(Q + 30) = 1000

Calculate the square root of the right side: 31.622776602

Break this problem into two subproblems by setting 
(Q + 30) equal to 31.622776602 and -31.622776602.

Subproblem 1

Q + 30 = 31.622776602 Simplifying Q + 30 = 31.622776602 Reorder the terms: 30 + Q = 31.622776602 Solving 30 + Q = 31.622776602 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + Q = 31.622776602 + -30 Combine like terms: 30 + -30 = 0 0 + Q = 31.622776602 + -30 Q = 31.622776602 + -30 Combine like terms: 31.622776602 + -30 = 1.622776602 Q = 1.622776602 Simplifying Q = 1.622776602

Subproblem 2

Q + 30 = -31.622776602 Simplifying Q + 30 = -31.622776602 Reorder the terms: 30 + Q = -31.622776602 Solving 30 + Q = -31.622776602 Solving for variable 'Q'. Move all terms containing Q to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + Q = -31.622776602 + -30 Combine like terms: 30 + -30 = 0 0 + Q = -31.622776602 + -30 Q = -31.622776602 + -30 Combine like terms: -31.622776602 + -30 = -61.622776602 Q = -61.622776602 Simplifying Q = -61.622776602

Solution

The solution to the problem is based on the solutions from the subproblems. Q = {1.622776602, -61.622776602}

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