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Simplifying -1200 = 2Q2 + 3Q Reorder the terms: -1200 = 3Q + 2Q2 Solving -1200 = 3Q + 2Q2 Solving for variable 'Q'. Reorder the terms: -1200 + -3Q + -2Q2 = 3Q + -3Q + 2Q2 + -2Q2 Combine like terms: 3Q + -3Q = 0 -1200 + -3Q + -2Q2 = 0 + 2Q2 + -2Q2 -1200 + -3Q + -2Q2 = 2Q2 + -2Q2 Combine like terms: 2Q2 + -2Q2 = 0 -1200 + -3Q + -2Q2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1200 + 3Q + 2Q2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1200 + 3Q + 2Q2)' equal to zero and attempt to solve: Simplifying 1200 + 3Q + 2Q2 = 0 Solving 1200 + 3Q + 2Q2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 600 + 1.5Q + Q2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + 1.5Q + -600 + Q2 = 0 + -600 Reorder the terms: 600 + -600 + 1.5Q + Q2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + 1.5Q + Q2 = 0 + -600 1.5Q + Q2 = 0 + -600 Combine like terms: 0 + -600 = -600 1.5Q + Q2 = -600 The Q term is 1.5Q. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5Q + 0.5625 + Q2 = -600 + 0.5625 Reorder the terms: 0.5625 + 1.5Q + Q2 = -600 + 0.5625 Combine like terms: -600 + 0.5625 = -599.4375 0.5625 + 1.5Q + Q2 = -599.4375 Factor a perfect square on the left side: (Q + 0.75)(Q + 0.75) = -599.4375 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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