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Simplifying -6q2 + -7q + 6 = 0 Reorder the terms: 6 + -7q + -6q2 = 0 Solving 6 + -7q + -6q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1 + 1.166666667q + q2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.166666667q + 1 + q2 = 0 + 1 Reorder the terms: -1 + 1 + 1.166666667q + q2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.166666667q + q2 = 0 + 1 1.166666667q + q2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.166666667q + q2 = 1 The q term is 1.166666667q. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667q + 0.3402777780 + q2 = 1 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667q + q2 = 1 + 0.3402777780 Combine like terms: 1 + 0.3402777780 = 1.340277778 0.3402777780 + 1.166666667q + q2 = 1.340277778 Factor a perfect square on the left side: (q + 0.5833333335)(q + 0.5833333335) = 1.340277778 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (q + 0.5833333335) equal to 1.157703666 and -1.157703666.Subproblem 1
q + 0.5833333335 = 1.157703666 Simplifying q + 0.5833333335 = 1.157703666 Reorder the terms: 0.5833333335 + q = 1.157703666 Solving 0.5833333335 + q = 1.157703666 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + q = 1.157703666 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + q = 1.157703666 + -0.5833333335 q = 1.157703666 + -0.5833333335 Combine like terms: 1.157703666 + -0.5833333335 = 0.5743703325 q = 0.5743703325 Simplifying q = 0.5743703325Subproblem 2
q + 0.5833333335 = -1.157703666 Simplifying q + 0.5833333335 = -1.157703666 Reorder the terms: 0.5833333335 + q = -1.157703666 Solving 0.5833333335 + q = -1.157703666 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + q = -1.157703666 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + q = -1.157703666 + -0.5833333335 q = -1.157703666 + -0.5833333335 Combine like terms: -1.157703666 + -0.5833333335 = -1.7410369995 q = -1.7410369995 Simplifying q = -1.7410369995Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.5743703325, -1.7410369995}
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