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Simplifying 0.05t2 + 54t + -500 = 0 Reorder the terms: -500 + 54t + 0.05t2 = 0 Solving -500 + 54t + 0.05t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -10000 + 1080t + t2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 1080t + 10000 + t2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 1080t + t2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 1080t + t2 = 0 + 10000 1080t + t2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 1080t + t2 = 10000 The t term is 1080t. Take half its coefficient (540). Square it (291600) and add it to both sides. Add '291600' to each side of the equation. 1080t + 291600 + t2 = 10000 + 291600 Reorder the terms: 291600 + 1080t + t2 = 10000 + 291600 Combine like terms: 10000 + 291600 = 301600 291600 + 1080t + t2 = 301600 Factor a perfect square on the left side: (t + 540)(t + 540) = 301600 Calculate the square root of the right side: 549.18120871 Break this problem into two subproblems by setting (t + 540) equal to 549.18120871 and -549.18120871.Subproblem 1
t + 540 = 549.18120871 Simplifying t + 540 = 549.18120871 Reorder the terms: 540 + t = 549.18120871 Solving 540 + t = 549.18120871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-540' to each side of the equation. 540 + -540 + t = 549.18120871 + -540 Combine like terms: 540 + -540 = 0 0 + t = 549.18120871 + -540 t = 549.18120871 + -540 Combine like terms: 549.18120871 + -540 = 9.18120871 t = 9.18120871 Simplifying t = 9.18120871Subproblem 2
t + 540 = -549.18120871 Simplifying t + 540 = -549.18120871 Reorder the terms: 540 + t = -549.18120871 Solving 540 + t = -549.18120871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-540' to each side of the equation. 540 + -540 + t = -549.18120871 + -540 Combine like terms: 540 + -540 = 0 0 + t = -549.18120871 + -540 t = -549.18120871 + -540 Combine like terms: -549.18120871 + -540 = -1089.18120871 t = -1089.18120871 Simplifying t = -1089.18120871Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.18120871, -1089.18120871}
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