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Simplifying 10t = -16t2 + 150t + 50 Reorder the terms: 10t = 50 + 150t + -16t2 Solving 10t = 50 + 150t + -16t2 Solving for variable 't'. Reorder the terms: -50 + 10t + -150t + 16t2 = 50 + 150t + -16t2 + -50 + -150t + 16t2 Combine like terms: 10t + -150t = -140t -50 + -140t + 16t2 = 50 + 150t + -16t2 + -50 + -150t + 16t2 Reorder the terms: -50 + -140t + 16t2 = 50 + -50 + 150t + -150t + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -50 + -140t + 16t2 = 0 + 150t + -150t + -16t2 + 16t2 -50 + -140t + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -50 + -140t + 16t2 = 0 + -16t2 + 16t2 -50 + -140t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -50 + -140t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + -70t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -70t + 8t2)' equal to zero and attempt to solve: Simplifying -25 + -70t + 8t2 = 0 Solving -25 + -70t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + -8.75t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -8.75t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -8.75t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -8.75t + t2 = 0 + 3.125 -8.75t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -8.75t + t2 = 3.125 The t term is -8.75t. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75t + 19.140625 + t2 = 3.125 + 19.140625 Reorder the terms: 19.140625 + -8.75t + t2 = 3.125 + 19.140625 Combine like terms: 3.125 + 19.140625 = 22.265625 19.140625 + -8.75t + t2 = 22.265625 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 22.265625 Calculate the square root of the right side: 4.718646522 Break this problem into two subproblems by setting (t + -4.375) equal to 4.718646522 and -4.718646522.Subproblem 1
t + -4.375 = 4.718646522 Simplifying t + -4.375 = 4.718646522 Reorder the terms: -4.375 + t = 4.718646522 Solving -4.375 + t = 4.718646522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = 4.718646522 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 4.718646522 + 4.375 t = 4.718646522 + 4.375 Combine like terms: 4.718646522 + 4.375 = 9.093646522 t = 9.093646522 Simplifying t = 9.093646522Subproblem 2
t + -4.375 = -4.718646522 Simplifying t + -4.375 = -4.718646522 Reorder the terms: -4.375 + t = -4.718646522 Solving -4.375 + t = -4.718646522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = -4.718646522 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -4.718646522 + 4.375 t = -4.718646522 + 4.375 Combine like terms: -4.718646522 + 4.375 = -0.343646522 t = -0.343646522 Simplifying t = -0.343646522Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.093646522, -0.343646522}Solution
t = {9.093646522, -0.343646522}
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