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Simplifying 50t + 0.05t2 = 1500 Solving 50t + 0.05t2 = 1500 Solving for variable 't'. Reorder the terms: -1500 + 50t + 0.05t2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 50t + 0.05t2 = 0 Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -30000 + 1000t + t2 = 0 Move the constant term to the right: Add '30000' to each side of the equation. -30000 + 1000t + 30000 + t2 = 0 + 30000 Reorder the terms: -30000 + 30000 + 1000t + t2 = 0 + 30000 Combine like terms: -30000 + 30000 = 0 0 + 1000t + t2 = 0 + 30000 1000t + t2 = 0 + 30000 Combine like terms: 0 + 30000 = 30000 1000t + t2 = 30000 The t term is 1000t. Take half its coefficient (500). Square it (250000) and add it to both sides. Add '250000' to each side of the equation. 1000t + 250000 + t2 = 30000 + 250000 Reorder the terms: 250000 + 1000t + t2 = 30000 + 250000 Combine like terms: 30000 + 250000 = 280000 250000 + 1000t + t2 = 280000 Factor a perfect square on the left side: (t + 500)(t + 500) = 280000 Calculate the square root of the right side: 529.150262213 Break this problem into two subproblems by setting (t + 500) equal to 529.150262213 and -529.150262213.Subproblem 1
t + 500 = 529.150262213 Simplifying t + 500 = 529.150262213 Reorder the terms: 500 + t = 529.150262213 Solving 500 + t = 529.150262213 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-500' to each side of the equation. 500 + -500 + t = 529.150262213 + -500 Combine like terms: 500 + -500 = 0 0 + t = 529.150262213 + -500 t = 529.150262213 + -500 Combine like terms: 529.150262213 + -500 = 29.150262213 t = 29.150262213 Simplifying t = 29.150262213Subproblem 2
t + 500 = -529.150262213 Simplifying t + 500 = -529.150262213 Reorder the terms: 500 + t = -529.150262213 Solving 500 + t = -529.150262213 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-500' to each side of the equation. 500 + -500 + t = -529.150262213 + -500 Combine like terms: 500 + -500 = 0 0 + t = -529.150262213 + -500 t = -529.150262213 + -500 Combine like terms: -529.150262213 + -500 = -1029.150262213 t = -1029.150262213 Simplifying t = -1029.150262213Solution
The solution to the problem is based on the solutions from the subproblems. t = {29.150262213, -1029.150262213}
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