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Simplifying 0 = (100 + -2Q) * Q + -20Q Reorder the terms for easier multiplication: 0 = Q(100 + -2Q) + -20Q 0 = (100 * Q + -2Q * Q) + -20Q 0 = (100Q + -2Q2) + -20Q Reorder the terms: 0 = 100Q + -20Q + -2Q2 Combine like terms: 100Q + -20Q = 80Q 0 = 80Q + -2Q2 Solving 0 = 80Q + -2Q2 Solving for variable 'Q'. Remove the zero: -80Q + 2Q2 = 80Q + -2Q2 + -80Q + 2Q2 Reorder the terms: -80Q + 2Q2 = 80Q + -80Q + -2Q2 + 2Q2 Combine like terms: 80Q + -80Q = 0 -80Q + 2Q2 = 0 + -2Q2 + 2Q2 -80Q + 2Q2 = -2Q2 + 2Q2 Combine like terms: -2Q2 + 2Q2 = 0 -80Q + 2Q2 = 0 Factor out the Greatest Common Factor (GCF), '2Q'. 2Q(-40 + Q) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'Q' equal to zero and attempt to solve: Simplifying Q = 0 Solving Q = 0 Move all terms containing Q to the left, all other terms to the right. Simplifying Q = 0Subproblem 2
Set the factor '(-40 + Q)' equal to zero and attempt to solve: Simplifying -40 + Q = 0 Solving -40 + Q = 0 Move all terms containing Q to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + Q = 0 + 40 Combine like terms: -40 + 40 = 0 0 + Q = 0 + 40 Q = 0 + 40 Combine like terms: 0 + 40 = 40 Q = 40 Simplifying Q = 40Solution
Q = {0, 40}
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