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Simplifying 0.04q2 + 8q + 200 = 0 Reorder the terms: 200 + 8q + 0.04q2 = 0 Solving 200 + 8q + 0.04q2 = 0 Solving for variable 'q'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 5000 + 200q + q2 = 0 Move the constant term to the right: Add '-5000' to each side of the equation. 5000 + 200q + -5000 + q2 = 0 + -5000 Reorder the terms: 5000 + -5000 + 200q + q2 = 0 + -5000 Combine like terms: 5000 + -5000 = 0 0 + 200q + q2 = 0 + -5000 200q + q2 = 0 + -5000 Combine like terms: 0 + -5000 = -5000 200q + q2 = -5000 The q term is 200q. Take half its coefficient (100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. 200q + 10000 + q2 = -5000 + 10000 Reorder the terms: 10000 + 200q + q2 = -5000 + 10000 Combine like terms: -5000 + 10000 = 5000 10000 + 200q + q2 = 5000 Factor a perfect square on the left side: (q + 100)(q + 100) = 5000 Calculate the square root of the right side: 70.710678119 Break this problem into two subproblems by setting (q + 100) equal to 70.710678119 and -70.710678119.Subproblem 1
q + 100 = 70.710678119 Simplifying q + 100 = 70.710678119 Reorder the terms: 100 + q = 70.710678119 Solving 100 + q = 70.710678119 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + q = 70.710678119 + -100 Combine like terms: 100 + -100 = 0 0 + q = 70.710678119 + -100 q = 70.710678119 + -100 Combine like terms: 70.710678119 + -100 = -29.289321881 q = -29.289321881 Simplifying q = -29.289321881Subproblem 2
q + 100 = -70.710678119 Simplifying q + 100 = -70.710678119 Reorder the terms: 100 + q = -70.710678119 Solving 100 + q = -70.710678119 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '-100' to each side of the equation. 100 + -100 + q = -70.710678119 + -100 Combine like terms: 100 + -100 = 0 0 + q = -70.710678119 + -100 q = -70.710678119 + -100 Combine like terms: -70.710678119 + -100 = -170.710678119 q = -170.710678119 Simplifying q = -170.710678119Solution
The solution to the problem is based on the solutions from the subproblems. q = {-29.289321881, -170.710678119}
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