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Simplifying t = -16t2 + 150t + 40 Reorder the terms: t = 40 + 150t + -16t2 Solving t = 40 + 150t + -16t2 Solving for variable 't'. Reorder the terms: -40 + t + -150t + 16t2 = 40 + 150t + -16t2 + -40 + -150t + 16t2 Combine like terms: t + -150t = -149t -40 + -149t + 16t2 = 40 + 150t + -16t2 + -40 + -150t + 16t2 Reorder the terms: -40 + -149t + 16t2 = 40 + -40 + 150t + -150t + -16t2 + 16t2 Combine like terms: 40 + -40 = 0 -40 + -149t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -40 + -149t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -40 + -149t + 16t2 = 0 + -16t2 + 16t2 -40 + -149t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -40 + -149t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.5 + -9.3125t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -9.3125t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -9.3125t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -9.3125t + t2 = 0 + 2.5 -9.3125t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -9.3125t + t2 = 2.5 The t term is -9.3125t. Take half its coefficient (-4.65625). Square it (21.68066406) and add it to both sides. Add '21.68066406' to each side of the equation. -9.3125t + 21.68066406 + t2 = 2.5 + 21.68066406 Reorder the terms: 21.68066406 + -9.3125t + t2 = 2.5 + 21.68066406 Combine like terms: 2.5 + 21.68066406 = 24.18066406 21.68066406 + -9.3125t + t2 = 24.18066406 Factor a perfect square on the left side: (t + -4.65625)(t + -4.65625) = 24.18066406 Calculate the square root of the right side: 4.917383863 Break this problem into two subproblems by setting (t + -4.65625) equal to 4.917383863 and -4.917383863.Subproblem 1
t + -4.65625 = 4.917383863 Simplifying t + -4.65625 = 4.917383863 Reorder the terms: -4.65625 + t = 4.917383863 Solving -4.65625 + t = 4.917383863 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.65625' to each side of the equation. -4.65625 + 4.65625 + t = 4.917383863 + 4.65625 Combine like terms: -4.65625 + 4.65625 = 0.00000 0.00000 + t = 4.917383863 + 4.65625 t = 4.917383863 + 4.65625 Combine like terms: 4.917383863 + 4.65625 = 9.573633863 t = 9.573633863 Simplifying t = 9.573633863Subproblem 2
t + -4.65625 = -4.917383863 Simplifying t + -4.65625 = -4.917383863 Reorder the terms: -4.65625 + t = -4.917383863 Solving -4.65625 + t = -4.917383863 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.65625' to each side of the equation. -4.65625 + 4.65625 + t = -4.917383863 + 4.65625 Combine like terms: -4.65625 + 4.65625 = 0.00000 0.00000 + t = -4.917383863 + 4.65625 t = -4.917383863 + 4.65625 Combine like terms: -4.917383863 + 4.65625 = -0.261133863 t = -0.261133863 Simplifying t = -0.261133863Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.573633863, -0.261133863}
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