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Simplifying (0.5q * q) + 20q + -7000 = 0 Multiply q * q (0.5q2) + 20q + -7000 = 0 Reorder the terms: -7000 + 20q + (0.5q2) = 0 Solving -7000 + 20q + (0.5q2) = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -14000 + 40q + q2 = 0 Move the constant term to the right: Add '14000' to each side of the equation. -14000 + 40q + 14000 + q2 = 0 + 14000 Reorder the terms: -14000 + 14000 + 40q + q2 = 0 + 14000 Combine like terms: -14000 + 14000 = 0 0 + 40q + q2 = 0 + 14000 40q + q2 = 0 + 14000 Combine like terms: 0 + 14000 = 14000 40q + q2 = 14000 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 = 14000 + 400 Reorder the terms: 400 + 40q + q2 = 14000 + 400 Combine like terms: 14000 + 400 = 14400 400 + 40q + q2 = 14400 Factor a perfect square on the left side: ((q) + 20)((q) + 20) = 14400 Calculate the square root of the right side: 120 Break this problem into two subproblems by setting ((q) + 20) equal to 120 and -120.Subproblem 1
(q) + 20 = 120 Simplifying (q) + 20 = 120 q + 20 = 120 Reorder the terms: 20 + q = 120 Solving 20 + q = 120 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 = 120 + -20 Combine like terms: 20 + -20 = 0 0 + q = 120 + -20 q = 120 + -20 Combine like terms: 120 + -20 = 100 q = 100 Simplifying q = 100Subproblem 2
(q) + 20 = -120 Simplifying (q) + 20 = -120 q + 20 = -120 Reorder the terms: 20 + q = -120 Solving 20 + q = -120 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 = -120 + -20 Combine like terms: 20 + -20 = 0 0 + q = -120 + -20 q = -120 + -20 Combine like terms: -120 + -20 = -140 q = -140 Simplifying q = -140Solution
The solution to the problem is based on the solutions from the subproblems. q = {100, -140}
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