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Simplifying 142 + 4Q + 4Q2 = 0 Solving 142 + 4Q + 4Q2 = 0 Solving for variable 'Q'. Factor out the Greatest Common Factor (GCF), '2'. 2(71 + 2Q + 2Q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(71 + 2Q + 2Q2)' equal to zero and attempt to solve: Simplifying 71 + 2Q + 2Q2 = 0 Solving 71 + 2Q + 2Q2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 35.5 + Q + Q2 = 0 Move the constant term to the right: Add '-35.5' to each side of the equation. 35.5 + Q + -35.5 + Q2 = 0 + -35.5 Reorder the terms: 35.5 + -35.5 + Q + Q2 = 0 + -35.5 Combine like terms: 35.5 + -35.5 = 0.0 0.0 + Q + Q2 = 0 + -35.5 Q + Q2 = 0 + -35.5 Combine like terms: 0 + -35.5 = -35.5 Q + Q2 = -35.5 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. + 0.25 + Q2 = -35.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + Q2 = -35.5 + 0.25 Combine like terms: -35.5 + 0.25 = -35.25 1.25 + Q2 = -35.25 Factor a perfect square on the left side: (Q + 0.5)(Q + 0.5) = -35.25 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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