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Simplifying 150 = 80q + -2q2 Solving 150 = 80q + -2q2 Solving for variable 'q'. Reorder the terms: 150 + -80q + 2q2 = 80q + -80q + -2q2 + 2q2 Combine like terms: 80q + -80q = 0 150 + -80q + 2q2 = 0 + -2q2 + 2q2 150 + -80q + 2q2 = -2q2 + 2q2 Combine like terms: -2q2 + 2q2 = 0 150 + -80q + 2q2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -40q + q2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + -40q + q2)' equal to zero and attempt to solve: Simplifying 75 + -40q + q2 = 0 Solving 75 + -40q + q2 = 0 Begin completing the square. Move the constant term to the right: Add '-75' to each side of the equation. 75 + -40q + -75 + q2 = 0 + -75 Reorder the terms: 75 + -75 + -40q + q2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -40q + q2 = 0 + -75 -40q + q2 = 0 + -75 Combine like terms: 0 + -75 = -75 -40q + q2 = -75 The q term is -40q. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40q + 400 + q2 = -75 + 400 Reorder the terms: 400 + -40q + q2 = -75 + 400 Combine like terms: -75 + 400 = 325 400 + -40q + q2 = 325 Factor a perfect square on the left side: (q + -20)(q + -20) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (q + -20) equal to 18.027756377 and -18.027756377.Subproblem 1
q + -20 = 18.027756377 Simplifying q + -20 = 18.027756377 Reorder the terms: -20 + q = 18.027756377 Solving -20 + q = 18.027756377 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + q = 18.027756377 + 20 Combine like terms: -20 + 20 = 0 0 + q = 18.027756377 + 20 q = 18.027756377 + 20 Combine like terms: 18.027756377 + 20 = 38.027756377 q = 38.027756377 Simplifying q = 38.027756377Subproblem 2
q + -20 = -18.027756377 Simplifying q + -20 = -18.027756377 Reorder the terms: -20 + q = -18.027756377 Solving -20 + q = -18.027756377 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + q = -18.027756377 + 20 Combine like terms: -20 + 20 = 0 0 + q = -18.027756377 + 20 q = -18.027756377 + 20 Combine like terms: -18.027756377 + 20 = 1.972243623 q = 1.972243623 Simplifying q = 1.972243623Solution
The solution to the problem is based on the solutions from the subproblems. q = {38.027756377, 1.972243623}Solution
q = {38.027756377, 1.972243623}
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