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Simplifying Q3 + -5Q2 + 60Q = 0 Reorder the terms: 60Q + -5Q2 + Q3 = 0 Solving 60Q + -5Q2 + Q3 = 0 Solving for variable 'Q'. Factor out the Greatest Common Factor (GCF), 'Q'. Q(60 + -5Q + Q2) = 0Subproblem 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 '(60 + -5Q + Q2)' equal to zero and attempt to solve: Simplifying 60 + -5Q + Q2 = 0 Solving 60 + -5Q + Q2 = 0 Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -5Q + -60 + Q2 = 0 + -60 Reorder the terms: 60 + -60 + -5Q + Q2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -5Q + Q2 = 0 + -60 -5Q + Q2 = 0 + -60 Combine like terms: 0 + -60 = -60 -5Q + Q2 = -60 The Q term is -5Q. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5Q + 6.25 + Q2 = -60 + 6.25 Reorder the terms: 6.25 + -5Q + Q2 = -60 + 6.25 Combine like terms: -60 + 6.25 = -53.75 6.25 + -5Q + Q2 = -53.75 Factor a perfect square on the left side: (Q + -2.5)(Q + -2.5) = -53.75 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.Solution
Q = {0}
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