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Simplifying 2q2 + 14q + 36 = 0 Reorder the terms: 36 + 14q + 2q2 = 0 Solving 36 + 14q + 2q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + 7q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + 7q + q2)' equal to zero and attempt to solve: Simplifying 18 + 7q + q2 = 0 Solving 18 + 7q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 7q + -18 + q2 = 0 + -18 Reorder the terms: 18 + -18 + 7q + q2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 7q + q2 = 0 + -18 7q + q2 = 0 + -18 Combine like terms: 0 + -18 = -18 7q + q2 = -18 The q term is 7q. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7q + 12.25 + q2 = -18 + 12.25 Reorder the terms: 12.25 + 7q + q2 = -18 + 12.25 Combine like terms: -18 + 12.25 = -5.75 12.25 + 7q + q2 = -5.75 Factor a perfect square on the left side: (q + 3.5)(q + 3.5) = -5.75 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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