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Simplifying 0 = 40q2 + -360q + 900 Reorder the terms: 0 = 900 + -360q + 40q2 Solving 0 = 900 + -360q + 40q2 Solving for variable 'q'. Combine like terms: 0 + -900 = -900 -900 + 360q + -40q2 = 900 + -360q + 40q2 + -900 + 360q + -40q2 Reorder the terms: -900 + 360q + -40q2 = 900 + -900 + -360q + 360q + 40q2 + -40q2 Combine like terms: 900 + -900 = 0 -900 + 360q + -40q2 = 0 + -360q + 360q + 40q2 + -40q2 -900 + 360q + -40q2 = -360q + 360q + 40q2 + -40q2 Combine like terms: -360q + 360q = 0 -900 + 360q + -40q2 = 0 + 40q2 + -40q2 -900 + 360q + -40q2 = 40q2 + -40q2 Combine like terms: 40q2 + -40q2 = 0 -900 + 360q + -40q2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-45 + 18q + -2q2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-45 + 18q + -2q2)' equal to zero and attempt to solve: Simplifying -45 + 18q + -2q2 = 0 Solving -45 + 18q + -2q2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 22.5 + -9q + q2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + -9q + -22.5 + q2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + -9q + q2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + -9q + q2 = 0 + -22.5 -9q + q2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 -9q + q2 = -22.5 The q term is -9q. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9q + 20.25 + q2 = -22.5 + 20.25 Reorder the terms: 20.25 + -9q + q2 = -22.5 + 20.25 Combine like terms: -22.5 + 20.25 = -2.25 20.25 + -9q + q2 = -2.25 Factor a perfect square on the left side: (q + -4.5)(q + -4.5) = -2.25 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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