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Simplifying 7q2 + -1q + -9 = 0 Reorder the terms: -9 + -1q + 7q2 = 0 Solving -9 + -1q + 7q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.285714286 + -0.1428571429q + q2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + -0.1428571429q + 1.285714286 + q2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + -0.1428571429q + q2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + -0.1428571429q + q2 = 0 + 1.285714286 -0.1428571429q + q2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 -0.1428571429q + q2 = 1.285714286 The q term is -0.1428571429q. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429q + 0.005102040819 + q2 = 1.285714286 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429q + q2 = 1.285714286 + 0.005102040819 Combine like terms: 1.285714286 + 0.005102040819 = 1.290816326819 0.005102040819 + -0.1428571429q + q2 = 1.290816326819 Factor a perfect square on the left side: (q + -0.07142857145)(q + -0.07142857145) = 1.290816326819 Calculate the square root of the right side: 1.13614098 Break this problem into two subproblems by setting (q + -0.07142857145) equal to 1.13614098 and -1.13614098.Subproblem 1
q + -0.07142857145 = 1.13614098 Simplifying q + -0.07142857145 = 1.13614098 Reorder the terms: -0.07142857145 + q = 1.13614098 Solving -0.07142857145 + q = 1.13614098 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + q = 1.13614098 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + q = 1.13614098 + 0.07142857145 q = 1.13614098 + 0.07142857145 Combine like terms: 1.13614098 + 0.07142857145 = 1.20756955145 q = 1.20756955145 Simplifying q = 1.20756955145Subproblem 2
q + -0.07142857145 = -1.13614098 Simplifying q + -0.07142857145 = -1.13614098 Reorder the terms: -0.07142857145 + q = -1.13614098 Solving -0.07142857145 + q = -1.13614098 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + q = -1.13614098 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + q = -1.13614098 + 0.07142857145 q = -1.13614098 + 0.07142857145 Combine like terms: -1.13614098 + 0.07142857145 = -1.06471240855 q = -1.06471240855 Simplifying q = -1.06471240855Solution
The solution to the problem is based on the solutions from the subproblems. q = {1.20756955145, -1.06471240855}
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