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Simplifying Q = 300 + -1Q + Q(Q + Q) Combine like terms: Q + Q = 2Q Q = 300 + -1Q + Q(2Q) Remove parenthesis around (2Q) Q = 300 + -1Q + Q * 2Q Reorder the terms for easier multiplication: Q = 300 + -1Q + 2Q * Q Multiply Q * Q Q = 300 + -1Q + 2Q2 Solving Q = 300 + -1Q + 2Q2 Solving for variable 'Q'. Reorder the terms: -300 + Q + Q + -2Q2 = 300 + -1Q + 2Q2 + -300 + Q + -2Q2 Combine like terms: Q + Q = 2Q -300 + 2Q + -2Q2 = 300 + -1Q + 2Q2 + -300 + Q + -2Q2 Reorder the terms: -300 + 2Q + -2Q2 = 300 + -300 + -1Q + Q + 2Q2 + -2Q2 Combine like terms: 300 + -300 = 0 -300 + 2Q + -2Q2 = 0 + -1Q + Q + 2Q2 + -2Q2 -300 + 2Q + -2Q2 = -1Q + Q + 2Q2 + -2Q2 Combine like terms: -1Q + Q = 0 -300 + 2Q + -2Q2 = 0 + 2Q2 + -2Q2 -300 + 2Q + -2Q2 = 2Q2 + -2Q2 Combine like terms: 2Q2 + -2Q2 = 0 -300 + 2Q + -2Q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-150 + Q + -1Q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-150 + Q + -1Q2)' equal to zero and attempt to solve: Simplifying -150 + Q + -1Q2 = 0 Solving -150 + Q + -1Q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 150 + -1Q + Q2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + -1Q + -150 + Q2 = 0 + -150 Reorder the terms: 150 + -150 + -1Q + Q2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + -1Q + Q2 = 0 + -150 -1Q + Q2 = 0 + -150 Combine like terms: 0 + -150 = -150 -1Q + Q2 = -150 The Q term is Q. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1Q + 0.25 + Q2 = -150 + 0.25 Reorder the terms: 0.25 + -1Q + Q2 = -150 + 0.25 Combine like terms: -150 + 0.25 = -149.75 0.25 + -1Q + Q2 = -149.75 Factor a perfect square on the left side: (Q + 0.5)(Q + 0.5) = -149.75 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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