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Simplifying 15q + -6q2 + q3 = 0 Solving 15q + -6q2 + q3 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), 'q'. q(15 + -6q + 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 '(15 + -6q + q2)' equal to zero and attempt to solve: Simplifying 15 + -6q + q2 = 0 Solving 15 + -6q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -6q + -15 + q2 = 0 + -15 Reorder the terms: 15 + -15 + -6q + q2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -6q + q2 = 0 + -15 -6q + q2 = 0 + -15 Combine like terms: 0 + -15 = -15 -6q + q2 = -15 The q term is -6q. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6q + 9 + q2 = -15 + 9 Reorder the terms: 9 + -6q + q2 = -15 + 9 Combine like terms: -15 + 9 = -6 9 + -6q + q2 = -6 Factor a perfect square on the left side: (q + -3)(q + -3) = -6 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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