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Simplifying 200 = 0.04t2 + 2t Reorder the terms: 200 = 2t + 0.04t2 Solving 200 = 2t + 0.04t2 Solving for variable 't'. Reorder the terms: 200 + -2t + -0.04t2 = 2t + -2t + 0.04t2 + -0.04t2 Combine like terms: 2t + -2t = 0 200 + -2t + -0.04t2 = 0 + 0.04t2 + -0.04t2 200 + -2t + -0.04t2 = 0.04t2 + -0.04t2 Combine like terms: 0.04t2 + -0.04t2 = 0.00 200 + -2t + -0.04t2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -5000 + 50t + t2 = 0 Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 50t + 5000 + t2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 50t + t2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 50t + t2 = 0 + 5000 50t + t2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 50t + t2 = 5000 The t term is 50t. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50t + 625 + t2 = 5000 + 625 Reorder the terms: 625 + 50t + t2 = 5000 + 625 Combine like terms: 5000 + 625 = 5625 625 + 50t + t2 = 5625 Factor a perfect square on the left side: (t + 25)(t + 25) = 5625 Calculate the square root of the right side: 75 Break this problem into two subproblems by setting (t + 25) equal to 75 and -75.Subproblem 1
t + 25 = 75 Simplifying t + 25 = 75 Reorder the terms: 25 + t = 75 Solving 25 + t = 75 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = 75 + -25 Combine like terms: 25 + -25 = 0 0 + t = 75 + -25 t = 75 + -25 Combine like terms: 75 + -25 = 50 t = 50 Simplifying t = 50Subproblem 2
t + 25 = -75 Simplifying t + 25 = -75 Reorder the terms: 25 + t = -75 Solving 25 + t = -75 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + t = -75 + -25 Combine like terms: 25 + -25 = 0 0 + t = -75 + -25 t = -75 + -25 Combine like terms: -75 + -25 = -100 t = -100 Simplifying t = -100Solution
The solution to the problem is based on the solutions from the subproblems. t = {50, -100}
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