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Simplifying -0.025q2 + 8.75q + -150 = 0 Reorder the terms: -150 + 8.75q + -0.025q2 = 0 Solving -150 + 8.75q + -0.025q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by -0.025 the coefficient of the squared term: Divide each side by '-0.025'. 6000 + -350q + q2 = 0 Move the constant term to the right: Add '-6000' to each side of the equation. 6000 + -350q + -6000 + q2 = 0 + -6000 Reorder the terms: 6000 + -6000 + -350q + q2 = 0 + -6000 Combine like terms: 6000 + -6000 = 0 0 + -350q + q2 = 0 + -6000 -350q + q2 = 0 + -6000 Combine like terms: 0 + -6000 = -6000 -350q + q2 = -6000 The q term is -350q. Take half its coefficient (-175). Square it (30625) and add it to both sides. Add '30625' to each side of the equation. -350q + 30625 + q2 = -6000 + 30625 Reorder the terms: 30625 + -350q + q2 = -6000 + 30625 Combine like terms: -6000 + 30625 = 24625 30625 + -350q + q2 = 24625 Factor a perfect square on the left side: (q + -175)(q + -175) = 24625 Calculate the square root of the right side: 156.923548265 Break this problem into two subproblems by setting (q + -175) equal to 156.923548265 and -156.923548265.Subproblem 1
q + -175 = 156.923548265 Simplifying q + -175 = 156.923548265 Reorder the terms: -175 + q = 156.923548265 Solving -175 + q = 156.923548265 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '175' to each side of the equation. -175 + 175 + q = 156.923548265 + 175 Combine like terms: -175 + 175 = 0 0 + q = 156.923548265 + 175 q = 156.923548265 + 175 Combine like terms: 156.923548265 + 175 = 331.923548265 q = 331.923548265 Simplifying q = 331.923548265Subproblem 2
q + -175 = -156.923548265 Simplifying q + -175 = -156.923548265 Reorder the terms: -175 + q = -156.923548265 Solving -175 + q = -156.923548265 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '175' to each side of the equation. -175 + 175 + q = -156.923548265 + 175 Combine like terms: -175 + 175 = 0 0 + q = -156.923548265 + 175 q = -156.923548265 + 175 Combine like terms: -156.923548265 + 175 = 18.076451735 q = 18.076451735 Simplifying q = 18.076451735Solution
The solution to the problem is based on the solutions from the subproblems. q = {331.923548265, 18.076451735}
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