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Simplifying 2q(q + -3) = 9 Reorder the terms: 2q(-3 + q) = 9 (-3 * 2q + q * 2q) = 9 (-6q + 2q2) = 9 Solving -6q + 2q2 = 9 Solving for variable 'q'. Reorder the terms: -9 + -6q + 2q2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -6q + 2q2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -3q + q2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -3q + 4.5 + q2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -3q + q2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -3q + q2 = 0 + 4.5 -3q + q2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -3q + q2 = 4.5 The q term is -3q. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3q + 2.25 + q2 = 4.5 + 2.25 Reorder the terms: 2.25 + -3q + q2 = 4.5 + 2.25 Combine like terms: 4.5 + 2.25 = 6.75 2.25 + -3q + q2 = 6.75 Factor a perfect square on the left side: (q + -1.5)(q + -1.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (q + -1.5) equal to 2.598076211 and -2.598076211.Subproblem 1
q + -1.5 = 2.598076211 Simplifying q + -1.5 = 2.598076211 Reorder the terms: -1.5 + q = 2.598076211 Solving -1.5 + q = 2.598076211 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + q = 2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + q = 2.598076211 + 1.5 q = 2.598076211 + 1.5 Combine like terms: 2.598076211 + 1.5 = 4.098076211 q = 4.098076211 Simplifying q = 4.098076211Subproblem 2
q + -1.5 = -2.598076211 Simplifying q + -1.5 = -2.598076211 Reorder the terms: -1.5 + q = -2.598076211 Solving -1.5 + q = -2.598076211 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + q = -2.598076211 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + q = -2.598076211 + 1.5 q = -2.598076211 + 1.5 Combine like terms: -2.598076211 + 1.5 = -1.098076211 q = -1.098076211 Simplifying q = -1.098076211Solution
The solution to the problem is based on the solutions from the subproblems. q = {4.098076211, -1.098076211}
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