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Simplifying -8q2 + 3q + 9 = 0 Reorder the terms: 9 + 3q + -8q2 = 0 Solving 9 + 3q + -8q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.125 + -0.375q + q2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -0.375q + 1.125 + q2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -0.375q + q2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -0.375q + q2 = 0 + 1.125 -0.375q + q2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -0.375q + q2 = 1.125 The q term is -0.375q. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375q + 0.03515625 + q2 = 1.125 + 0.03515625 Reorder the terms: 0.03515625 + -0.375q + q2 = 1.125 + 0.03515625 Combine like terms: 1.125 + 0.03515625 = 1.16015625 0.03515625 + -0.375q + q2 = 1.16015625 Factor a perfect square on the left side: (q + -0.1875)(q + -0.1875) = 1.16015625 Calculate the square root of the right side: 1.077105496 Break this problem into two subproblems by setting (q + -0.1875) equal to 1.077105496 and -1.077105496.Subproblem 1
q + -0.1875 = 1.077105496 Simplifying q + -0.1875 = 1.077105496 Reorder the terms: -0.1875 + q = 1.077105496 Solving -0.1875 + q = 1.077105496 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + q = 1.077105496 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + q = 1.077105496 + 0.1875 q = 1.077105496 + 0.1875 Combine like terms: 1.077105496 + 0.1875 = 1.264605496 q = 1.264605496 Simplifying q = 1.264605496Subproblem 2
q + -0.1875 = -1.077105496 Simplifying q + -0.1875 = -1.077105496 Reorder the terms: -0.1875 + q = -1.077105496 Solving -0.1875 + q = -1.077105496 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + q = -1.077105496 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + q = -1.077105496 + 0.1875 q = -1.077105496 + 0.1875 Combine like terms: -1.077105496 + 0.1875 = -0.889605496 q = -0.889605496 Simplifying q = -0.889605496Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.264605496, -0.889605496}
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