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Simplifying -150 = 40Q + 3Q2 Solving -150 = 40Q + 3Q2 Solving for variable 'Q'. Reorder the terms: -150 + -40Q + -3Q2 = 40Q + -40Q + 3Q2 + -3Q2 Combine like terms: 40Q + -40Q = 0 -150 + -40Q + -3Q2 = 0 + 3Q2 + -3Q2 -150 + -40Q + -3Q2 = 3Q2 + -3Q2 Combine like terms: 3Q2 + -3Q2 = 0 -150 + -40Q + -3Q2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(150 + 40Q + 3Q2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(150 + 40Q + 3Q2)' equal to zero and attempt to solve: Simplifying 150 + 40Q + 3Q2 = 0 Solving 150 + 40Q + 3Q2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 50 + 13.33333333Q + Q2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + 13.33333333Q + -50 + Q2 = 0 + -50 Reorder the terms: 50 + -50 + 13.33333333Q + Q2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 13.33333333Q + Q2 = 0 + -50 13.33333333Q + Q2 = 0 + -50 Combine like terms: 0 + -50 = -50 13.33333333Q + Q2 = -50 The Q term is 13.33333333Q. Take half its coefficient (6.666666665). Square it (44.44444442) and add it to both sides. Add '44.44444442' to each side of the equation. 13.33333333Q + 44.44444442 + Q2 = -50 + 44.44444442 Reorder the terms: 44.44444442 + 13.33333333Q + Q2 = -50 + 44.44444442 Combine like terms: -50 + 44.44444442 = -5.55555558 44.44444442 + 13.33333333Q + Q2 = -5.55555558 Factor a perfect square on the left side: (Q + 6.666666665)(Q + 6.666666665) = -5.55555558 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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