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Simplifying 15t + 2t2 = 100 Solving 15t + 2t2 = 100 Solving for variable 't'. Reorder the terms: -100 + 15t + 2t2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 15t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + 7.5t + t2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + 7.5t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + 7.5t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 7.5t + t2 = 0 + 50 7.5t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 7.5t + t2 = 50 The t term is 7.5t. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5t + 14.0625 + t2 = 50 + 14.0625 Reorder the terms: 14.0625 + 7.5t + t2 = 50 + 14.0625 Combine like terms: 50 + 14.0625 = 64.0625 14.0625 + 7.5t + t2 = 64.0625 Factor a perfect square on the left side: (t + 3.75)(t + 3.75) = 64.0625 Calculate the square root of the right side: 8.003905297 Break this problem into two subproblems by setting (t + 3.75) equal to 8.003905297 and -8.003905297.Subproblem 1
t + 3.75 = 8.003905297 Simplifying t + 3.75 = 8.003905297 Reorder the terms: 3.75 + t = 8.003905297 Solving 3.75 + t = 8.003905297 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + t = 8.003905297 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + t = 8.003905297 + -3.75 t = 8.003905297 + -3.75 Combine like terms: 8.003905297 + -3.75 = 4.253905297 t = 4.253905297 Simplifying t = 4.253905297Subproblem 2
t + 3.75 = -8.003905297 Simplifying t + 3.75 = -8.003905297 Reorder the terms: 3.75 + t = -8.003905297 Solving 3.75 + t = -8.003905297 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + t = -8.003905297 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + t = -8.003905297 + -3.75 t = -8.003905297 + -3.75 Combine like terms: -8.003905297 + -3.75 = -11.753905297 t = -11.753905297 Simplifying t = -11.753905297Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.253905297, -11.753905297}
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