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Simplifying 150(t) = 16.1t2 + 150 Reorder the terms: 150t = 150 + 16.1t2 Solving 150t = 150 + 16.1t2 Solving for variable 't'. Reorder the terms: -150 + 150t + -16.1t2 = 150 + 16.1t2 + -150 + -16.1t2 Reorder the terms: -150 + 150t + -16.1t2 = 150 + -150 + 16.1t2 + -16.1t2 Combine like terms: 150 + -150 = 0 -150 + 150t + -16.1t2 = 0 + 16.1t2 + -16.1t2 -150 + 150t + -16.1t2 = 16.1t2 + -16.1t2 Combine like terms: 16.1t2 + -16.1t2 = 0.0 -150 + 150t + -16.1t2 = 0.0 Begin completing the square. Divide all terms by -16.1 the coefficient of the squared term: Divide each side by '-16.1'. 9.316770186 + -9.316770186t + t2 = 0 Move the constant term to the right: Add '-9.316770186' to each side of the equation. 9.316770186 + -9.316770186t + -9.316770186 + t2 = 0 + -9.316770186 Reorder the terms: 9.316770186 + -9.316770186 + -9.316770186t + t2 = 0 + -9.316770186 Combine like terms: 9.316770186 + -9.316770186 = 0.000000000 0.000000000 + -9.316770186t + t2 = 0 + -9.316770186 -9.316770186t + t2 = 0 + -9.316770186 Combine like terms: 0 + -9.316770186 = -9.316770186 -9.316770186t + t2 = -9.316770186 The t term is -9.316770186t. Take half its coefficient (-4.658385093). Square it (21.70055167) and add it to both sides. Add '21.70055167' to each side of the equation. -9.316770186t + 21.70055167 + t2 = -9.316770186 + 21.70055167 Reorder the terms: 21.70055167 + -9.316770186t + t2 = -9.316770186 + 21.70055167 Combine like terms: -9.316770186 + 21.70055167 = 12.383781484 21.70055167 + -9.316770186t + t2 = 12.383781484 Factor a perfect square on the left side: (t + -4.658385093)(t + -4.658385093) = 12.383781484 Calculate the square root of the right side: 3.519059744 Break this problem into two subproblems by setting (t + -4.658385093) equal to 3.519059744 and -3.519059744.Subproblem 1
t + -4.658385093 = 3.519059744 Simplifying t + -4.658385093 = 3.519059744 Reorder the terms: -4.658385093 + t = 3.519059744 Solving -4.658385093 + t = 3.519059744 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.658385093' to each side of the equation. -4.658385093 + 4.658385093 + t = 3.519059744 + 4.658385093 Combine like terms: -4.658385093 + 4.658385093 = 0.000000000 0.000000000 + t = 3.519059744 + 4.658385093 t = 3.519059744 + 4.658385093 Combine like terms: 3.519059744 + 4.658385093 = 8.177444837 t = 8.177444837 Simplifying t = 8.177444837Subproblem 2
t + -4.658385093 = -3.519059744 Simplifying t + -4.658385093 = -3.519059744 Reorder the terms: -4.658385093 + t = -3.519059744 Solving -4.658385093 + t = -3.519059744 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.658385093' to each side of the equation. -4.658385093 + 4.658385093 + t = -3.519059744 + 4.658385093 Combine like terms: -4.658385093 + 4.658385093 = 0.000000000 0.000000000 + t = -3.519059744 + 4.658385093 t = -3.519059744 + 4.658385093 Combine like terms: -3.519059744 + 4.658385093 = 1.139325349 t = 1.139325349 Simplifying t = 1.139325349Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.177444837, 1.139325349}
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