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Simplifying 12q2 + 5q + -5 = 0 Reorder the terms: -5 + 5q + 12q2 = 0 Solving -5 + 5q + 12q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + 0.4166666667q + q2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667q + 0.4166666667 + q2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + 0.4166666667q + q2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + 0.4166666667q + q2 = 0 + 0.4166666667 0.4166666667q + q2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 0.4166666667q + q2 = 0.4166666667 The q term is 0.4166666667q. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667q + 0.04340277781 + q2 = 0.4166666667 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667q + q2 = 0.4166666667 + 0.04340277781 Combine like terms: 0.4166666667 + 0.04340277781 = 0.46006944451 0.04340277781 + 0.4166666667q + q2 = 0.46006944451 Factor a perfect square on the left side: (q + 0.2083333334)(q + 0.2083333334) = 0.46006944451 Calculate the square root of the right side: 0.678284192 Break this problem into two subproblems by setting (q + 0.2083333334) equal to 0.678284192 and -0.678284192.Subproblem 1
q + 0.2083333334 = 0.678284192 Simplifying q + 0.2083333334 = 0.678284192 Reorder the terms: 0.2083333334 + q = 0.678284192 Solving 0.2083333334 + q = 0.678284192 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + q = 0.678284192 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + q = 0.678284192 + -0.2083333334 q = 0.678284192 + -0.2083333334 Combine like terms: 0.678284192 + -0.2083333334 = 0.4699508586 q = 0.4699508586 Simplifying q = 0.4699508586Subproblem 2
q + 0.2083333334 = -0.678284192 Simplifying q + 0.2083333334 = -0.678284192 Reorder the terms: 0.2083333334 + q = -0.678284192 Solving 0.2083333334 + q = -0.678284192 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + q = -0.678284192 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + q = -0.678284192 + -0.2083333334 q = -0.678284192 + -0.2083333334 Combine like terms: -0.678284192 + -0.2083333334 = -0.8866175254 q = -0.8866175254 Simplifying q = -0.8866175254Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.4699508586, -0.8866175254}
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