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Simplifying -11.8 = 5q(-2 + -8q) + -8.8q -11.8 = (-2 * 5q + -8q * 5q) + -8.8q -11.8 = (-10q + -40q2) + -8.8q Reorder the terms: -11.8 = -10q + -8.8q + -40q2 Combine like terms: -10q + -8.8q = -18.8q -11.8 = -18.8q + -40q2 Solving -11.8 = -18.8q + -40q2 Solving for variable 'q'. Reorder the terms: -11.8 + 18.8q + 40q2 = -18.8q + 18.8q + -40q2 + 40q2 Combine like terms: -18.8q + 18.8q = 0.0 -11.8 + 18.8q + 40q2 = 0.0 + -40q2 + 40q2 -11.8 + 18.8q + 40q2 = -40q2 + 40q2 Combine like terms: -40q2 + 40q2 = 0 -11.8 + 18.8q + 40q2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.295 + 0.47q + q2 = 0 Move the constant term to the right: Add '0.295' to each side of the equation. -0.295 + 0.47q + 0.295 + q2 = 0 + 0.295 Reorder the terms: -0.295 + 0.295 + 0.47q + q2 = 0 + 0.295 Combine like terms: -0.295 + 0.295 = 0.000 0.000 + 0.47q + q2 = 0 + 0.295 0.47q + q2 = 0 + 0.295 Combine like terms: 0 + 0.295 = 0.295 0.47q + q2 = 0.295 The q term is 0.47q. Take half its coefficient (0.235). Square it (0.055225) and add it to both sides. Add '0.055225' to each side of the equation. 0.47q + 0.055225 + q2 = 0.295 + 0.055225 Reorder the terms: 0.055225 + 0.47q + q2 = 0.295 + 0.055225 Combine like terms: 0.295 + 0.055225 = 0.350225 0.055225 + 0.47q + q2 = 0.350225 Factor a perfect square on the left side: (q + 0.235)(q + 0.235) = 0.350225 Calculate the square root of the right side: 0.591798107 Break this problem into two subproblems by setting (q + 0.235) equal to 0.591798107 and -0.591798107.Subproblem 1
q + 0.235 = 0.591798107 Simplifying q + 0.235 = 0.591798107 Reorder the terms: 0.235 + q = 0.591798107 Solving 0.235 + q = 0.591798107 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.235' to each side of the equation. 0.235 + -0.235 + q = 0.591798107 + -0.235 Combine like terms: 0.235 + -0.235 = 0.000 0.000 + q = 0.591798107 + -0.235 q = 0.591798107 + -0.235 Combine like terms: 0.591798107 + -0.235 = 0.356798107 q = 0.356798107 Simplifying q = 0.356798107Subproblem 2
q + 0.235 = -0.591798107 Simplifying q + 0.235 = -0.591798107 Reorder the terms: 0.235 + q = -0.591798107 Solving 0.235 + q = -0.591798107 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-0.235' to each side of the equation. 0.235 + -0.235 + q = -0.591798107 + -0.235 Combine like terms: 0.235 + -0.235 = 0.000 0.000 + q = -0.591798107 + -0.235 q = -0.591798107 + -0.235 Combine like terms: -0.591798107 + -0.235 = -0.826798107 q = -0.826798107 Simplifying q = -0.826798107Solution
The solution to the problem is based on the solutions from the subproblems. q = {0.356798107, -0.826798107}
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