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Simplifying 2q2 + -8 = 3q Reorder the terms: -8 + 2q2 = 3q Solving -8 + 2q2 = 3q Solving for variable 'q'. Reorder the terms: -8 + -3q + 2q2 = 3q + -3q Combine like terms: 3q + -3q = 0 -8 + -3q + 2q2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4 + -1.5q + q2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.5q + 4 + q2 = 0 + 4 Reorder the terms: -4 + 4 + -1.5q + q2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.5q + q2 = 0 + 4 -1.5q + q2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.5q + q2 = 4 The q term is -1.5q. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5q + 0.5625 + q2 = 4 + 0.5625 Reorder the terms: 0.5625 + -1.5q + q2 = 4 + 0.5625 Combine like terms: 4 + 0.5625 = 4.5625 0.5625 + -1.5q + q2 = 4.5625 Factor a perfect square on the left side: (q + -0.75)(q + -0.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (q + -0.75) equal to 2.136000936 and -2.136000936.Subproblem 1
q + -0.75 = 2.136000936 Simplifying q + -0.75 = 2.136000936 Reorder the terms: -0.75 + q = 2.136000936 Solving -0.75 + q = 2.136000936 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + q = 2.136000936 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + q = 2.136000936 + 0.75 q = 2.136000936 + 0.75 Combine like terms: 2.136000936 + 0.75 = 2.886000936 q = 2.886000936 Simplifying q = 2.886000936Subproblem 2
q + -0.75 = -2.136000936 Simplifying q + -0.75 = -2.136000936 Reorder the terms: -0.75 + q = -2.136000936 Solving -0.75 + q = -2.136000936 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + q = -2.136000936 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + q = -2.136000936 + 0.75 q = -2.136000936 + 0.75 Combine like terms: -2.136000936 + 0.75 = -1.386000936 q = -1.386000936 Simplifying q = -1.386000936Solution
The solution to the problem is based on the solutions from the subproblems. q = {2.886000936, -1.386000936}
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