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Simplifying 2q2 + 36q = -82 Reorder the terms: 36q + 2q2 = -82 Solving 36q + 2q2 = -82 Solving for variable 'q'. Reorder the terms: 82 + 36q + 2q2 = -82 + 82 Combine like terms: -82 + 82 = 0 82 + 36q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(41 + 18q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + 18q + q2)' equal to zero and attempt to solve: Simplifying 41 + 18q + q2 = 0 Solving 41 + 18q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 18q + -41 + q2 = 0 + -41 Reorder the terms: 41 + -41 + 18q + q2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 18q + q2 = 0 + -41 18q + q2 = 0 + -41 Combine like terms: 0 + -41 = -41 18q + q2 = -41 The q term is 18q. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18q + 81 + q2 = -41 + 81 Reorder the terms: 81 + 18q + q2 = -41 + 81 Combine like terms: -41 + 81 = 40 81 + 18q + q2 = 40 Factor a perfect square on the left side: (q + 9)(q + 9) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (q + 9) equal to 6.32455532 and -6.32455532.Subproblem 1
q + 9 = 6.32455532 Simplifying q + 9 = 6.32455532 Reorder the terms: 9 + q = 6.32455532 Solving 9 + q = 6.32455532 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + q = 6.32455532 + -9 Combine like terms: 9 + -9 = 0 0 + q = 6.32455532 + -9 q = 6.32455532 + -9 Combine like terms: 6.32455532 + -9 = -2.67544468 q = -2.67544468 Simplifying q = -2.67544468Subproblem 2
q + 9 = -6.32455532 Simplifying q + 9 = -6.32455532 Reorder the terms: 9 + q = -6.32455532 Solving 9 + q = -6.32455532 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + q = -6.32455532 + -9 Combine like terms: 9 + -9 = 0 0 + q = -6.32455532 + -9 q = -6.32455532 + -9 Combine like terms: -6.32455532 + -9 = -15.32455532 q = -15.32455532 Simplifying q = -15.32455532Solution
The solution to the problem is based on the solutions from the subproblems. q = {-2.67544468, -15.32455532}Solution
q = {-2.67544468, -15.32455532}
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