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Simplifying -3q2 + -6q + -45 = 0 Reorder the terms: -45 + -6q + -3q2 = 0 Solving -45 + -6q + -3q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '-3'. -3(15 + 2q + q2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(15 + 2q + q2)' equal to zero and attempt to solve: Simplifying 15 + 2q + q2 = 0 Solving 15 + 2q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 2q + -15 + q2 = 0 + -15 Reorder the terms: 15 + -15 + 2q + q2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2q + q2 = 0 + -15 2q + q2 = 0 + -15 Combine like terms: 0 + -15 = -15 2q + q2 = -15 The q term is 2q. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2q + 1 + q2 = -15 + 1 Reorder the terms: 1 + 2q + q2 = -15 + 1 Combine like terms: -15 + 1 = -14 1 + 2q + q2 = -14 Factor a perfect square on the left side: (q + 1)(q + 1) = -14 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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