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Simplifying -0.005q2 + 2.5q = 300 Reorder the terms: 2.5q + -0.005q2 = 300 Solving 2.5q + -0.005q2 = 300 Solving for variable 'q'. Reorder the terms: -300 + 2.5q + -0.005q2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 2.5q + -0.005q2 = 0 Begin completing the square. Divide all terms by -0.005 the coefficient of the squared term: Divide each side by '-0.005'. 60000 + -500q + q2 = 0 Move the constant term to the right: Add '-60000' to each side of the equation. 60000 + -500q + -60000 + q2 = 0 + -60000 Reorder the terms: 60000 + -60000 + -500q + q2 = 0 + -60000 Combine like terms: 60000 + -60000 = 0 0 + -500q + q2 = 0 + -60000 -500q + q2 = 0 + -60000 Combine like terms: 0 + -60000 = -60000 -500q + q2 = -60000 The q term is -500q. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500q + 62500 + q2 = -60000 + 62500 Reorder the terms: 62500 + -500q + q2 = -60000 + 62500 Combine like terms: -60000 + 62500 = 2500 62500 + -500q + q2 = 2500 Factor a perfect square on the left side: (q + -250)(q + -250) = 2500 Calculate the square root of the right side: 50 Break this problem into two subproblems by setting (q + -250) equal to 50 and -50.Subproblem 1
q + -250 = 50 Simplifying q + -250 = 50 Reorder the terms: -250 + q = 50 Solving -250 + q = 50 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + q = 50 + 250 Combine like terms: -250 + 250 = 0 0 + q = 50 + 250 q = 50 + 250 Combine like terms: 50 + 250 = 300 q = 300 Simplifying q = 300Subproblem 2
q + -250 = -50 Simplifying q + -250 = -50 Reorder the terms: -250 + q = -50 Solving -250 + q = -50 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '250' to each side of the equation. -250 + 250 + q = -50 + 250 Combine like terms: -250 + 250 = 0 0 + q = -50 + 250 q = -50 + 250 Combine like terms: -50 + 250 = 200 q = 200 Simplifying q = 200Solution
The solution to the problem is based on the solutions from the subproblems. q = {300, 200}
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