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Simplifying 3q2 + -36q + 7500 = 0 Reorder the terms: 7500 + -36q + 3q2 = 0 Solving 7500 + -36q + 3q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(2500 + -12q + q2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2500 + -12q + q2)' equal to zero and attempt to solve: Simplifying 2500 + -12q + q2 = 0 Solving 2500 + -12q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-2500' to each side of the equation. 2500 + -12q + -2500 + q2 = 0 + -2500 Reorder the terms: 2500 + -2500 + -12q + q2 = 0 + -2500 Combine like terms: 2500 + -2500 = 0 0 + -12q + q2 = 0 + -2500 -12q + q2 = 0 + -2500 Combine like terms: 0 + -2500 = -2500 -12q + q2 = -2500 The q term is -12q. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12q + 36 + q2 = -2500 + 36 Reorder the terms: 36 + -12q + q2 = -2500 + 36 Combine like terms: -2500 + 36 = -2464 36 + -12q + q2 = -2464 Factor a perfect square on the left side: (q + -6)(q + -6) = -2464 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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