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Simplifying 18q + -2q2 + -18 = 0 Reorder the terms: -18 + 18q + -2q2 = 0 Solving -18 + 18q + -2q2 = 0 Solving for variable 'q'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 9q + -1q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 9q + -1q2)' equal to zero and attempt to solve: Simplifying -9 + 9q + -1q2 = 0 Solving -9 + 9q + -1q2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -9q + q2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -9q + -9 + q2 = 0 + -9 Reorder the terms: 9 + -9 + -9q + q2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -9q + q2 = 0 + -9 -9q + q2 = 0 + -9 Combine like terms: 0 + -9 = -9 -9q + q2 = -9 The q term is -9q. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9q + 20.25 + q2 = -9 + 20.25 Reorder the terms: 20.25 + -9q + q2 = -9 + 20.25 Combine like terms: -9 + 20.25 = 11.25 20.25 + -9q + q2 = 11.25 Factor a perfect square on the left side: (q + -4.5)(q + -4.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (q + -4.5) equal to 3.354101966 and -3.354101966.Subproblem 1
q + -4.5 = 3.354101966 Simplifying q + -4.5 = 3.354101966 Reorder the terms: -4.5 + q = 3.354101966 Solving -4.5 + q = 3.354101966 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + q = 3.354101966 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + q = 3.354101966 + 4.5 q = 3.354101966 + 4.5 Combine like terms: 3.354101966 + 4.5 = 7.854101966 q = 7.854101966 Simplifying q = 7.854101966Subproblem 2
q + -4.5 = -3.354101966 Simplifying q + -4.5 = -3.354101966 Reorder the terms: -4.5 + q = -3.354101966 Solving -4.5 + q = -3.354101966 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + q = -3.354101966 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + q = -3.354101966 + 4.5 q = -3.354101966 + 4.5 Combine like terms: -3.354101966 + 4.5 = 1.145898034 q = 1.145898034 Simplifying q = 1.145898034Solution
The solution to the problem is based on the solutions from the subproblems. q = {7.854101966, 1.145898034}Solution
q = {7.854101966, 1.145898034}
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