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Simplifying 2q2 + 12q + -27 = 0 Reorder the terms: -27 + 12q + 2q2 = 0 Solving -27 + 12q + 2q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 6q + q2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 6q + 13.5 + q2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 6q + q2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 6q + q2 = 0 + 13.5 6q + q2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 6q + q2 = 13.5 The q term is 6q. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6q + 9 + q2 = 13.5 + 9 Reorder the terms: 9 + 6q + q2 = 13.5 + 9 Combine like terms: 13.5 + 9 = 22.5 9 + 6q + q2 = 22.5 Factor a perfect square on the left side: (q + 3)(q + 3) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (q + 3) equal to 4.74341649 and -4.74341649.Subproblem 1
q + 3 = 4.74341649 Simplifying q + 3 = 4.74341649 Reorder the terms: 3 + q = 4.74341649 Solving 3 + q = 4.74341649 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + q = 4.74341649 + -3 Combine like terms: 3 + -3 = 0 0 + q = 4.74341649 + -3 q = 4.74341649 + -3 Combine like terms: 4.74341649 + -3 = 1.74341649 q = 1.74341649 Simplifying q = 1.74341649Subproblem 2
q + 3 = -4.74341649 Simplifying q + 3 = -4.74341649 Reorder the terms: 3 + q = -4.74341649 Solving 3 + q = -4.74341649 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + q = -4.74341649 + -3 Combine like terms: 3 + -3 = 0 0 + q = -4.74341649 + -3 q = -4.74341649 + -3 Combine like terms: -4.74341649 + -3 = -7.74341649 q = -7.74341649 Simplifying q = -7.74341649Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.74341649, -7.74341649}
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