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Simplifying 3q2 + 3q + 36 = 0 Reorder the terms: 36 + 3q + 3q2 = 0 Solving 36 + 3q + 3q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + q + q2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(12 + q + q2)' equal to zero and attempt to solve: Simplifying 12 + q + q2 = 0 Solving 12 + q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + q + -12 + q2 = 0 + -12 Reorder the terms: 12 + -12 + q + q2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + q + q2 = 0 + -12 q + q2 = 0 + -12 Combine like terms: 0 + -12 = -12 q + q2 = -12 The q term is q. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. q + 0.25 + q2 = -12 + 0.25 Reorder the terms: 0.25 + q + q2 = -12 + 0.25 Combine like terms: -12 + 0.25 = -11.75 0.25 + q + q2 = -11.75 Factor a perfect square on the left side: (q + 0.5)(q + 0.5) = -11.75 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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