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Simplifying -4q2 = 10q + 2400 Reorder the terms: -4q2 = 2400 + 10q Solving -4q2 = 2400 + 10q Solving for variable 'q'. Reorder the terms: -2400 + -10q + -4q2 = 2400 + 10q + -2400 + -10q Reorder the terms: -2400 + -10q + -4q2 = 2400 + -2400 + 10q + -10q Combine like terms: 2400 + -2400 = 0 -2400 + -10q + -4q2 = 0 + 10q + -10q -2400 + -10q + -4q2 = 10q + -10q Combine like terms: 10q + -10q = 0 -2400 + -10q + -4q2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(1200 + 5q + 2q2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(1200 + 5q + 2q2)' equal to zero and attempt to solve: Simplifying 1200 + 5q + 2q2 = 0 Solving 1200 + 5q + 2q2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 600 + 2.5q + q2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + 2.5q + -600 + q2 = 0 + -600 Reorder the terms: 600 + -600 + 2.5q + q2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + 2.5q + q2 = 0 + -600 2.5q + q2 = 0 + -600 Combine like terms: 0 + -600 = -600 2.5q + q2 = -600 The q term is 2.5q. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5q + 1.5625 + q2 = -600 + 1.5625 Reorder the terms: 1.5625 + 2.5q + q2 = -600 + 1.5625 Combine like terms: -600 + 1.5625 = -598.4375 1.5625 + 2.5q + q2 = -598.4375 Factor a perfect square on the left side: (q + 1.25)(q + 1.25) = -598.4375 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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