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Simplifying 7q2 + 9q + -9 = 0 Reorder the terms: -9 + 9q + 7q2 = 0 Solving -9 + 9q + 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 + 1.285714286q + q2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 1.285714286q + 1.285714286 + q2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 1.285714286q + q2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 1.285714286q + q2 = 0 + 1.285714286 1.285714286q + q2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 1.285714286q + q2 = 1.285714286 The q term is 1.285714286q. Take half its coefficient (0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. 1.285714286q + 0.4132653063 + q2 = 1.285714286 + 0.4132653063 Reorder the terms: 0.4132653063 + 1.285714286q + q2 = 1.285714286 + 0.4132653063 Combine like terms: 1.285714286 + 0.4132653063 = 1.6989795923 0.4132653063 + 1.285714286q + q2 = 1.6989795923 Factor a perfect square on the left side: (q + 0.642857143)(q + 0.642857143) = 1.6989795923 Calculate the square root of the right side: 1.303449114 Break this problem into two subproblems by setting (q + 0.642857143) equal to 1.303449114 and -1.303449114.Subproblem 1
q + 0.642857143 = 1.303449114 Simplifying q + 0.642857143 = 1.303449114 Reorder the terms: 0.642857143 + q = 1.303449114 Solving 0.642857143 + q = 1.303449114 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + q = 1.303449114 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + q = 1.303449114 + -0.642857143 q = 1.303449114 + -0.642857143 Combine like terms: 1.303449114 + -0.642857143 = 0.660591971 q = 0.660591971 Simplifying q = 0.660591971Subproblem 2
q + 0.642857143 = -1.303449114 Simplifying q + 0.642857143 = -1.303449114 Reorder the terms: 0.642857143 + q = -1.303449114 Solving 0.642857143 + q = -1.303449114 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + q = -1.303449114 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + q = -1.303449114 + -0.642857143 q = -1.303449114 + -0.642857143 Combine like terms: -1.303449114 + -0.642857143 = -1.946306257 q = -1.946306257 Simplifying q = -1.946306257Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.660591971, -1.946306257}
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