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Simplifying 150 = -16t2 + 117t + 3 Reorder the terms: 150 = 3 + 117t + -16t2 Solving 150 = 3 + 117t + -16t2 Solving for variable 't'. Combine like terms: 150 + -3 = 147 147 + -117t + 16t2 = 3 + 117t + -16t2 + -3 + -117t + 16t2 Reorder the terms: 147 + -117t + 16t2 = 3 + -3 + 117t + -117t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 147 + -117t + 16t2 = 0 + 117t + -117t + -16t2 + 16t2 147 + -117t + 16t2 = 117t + -117t + -16t2 + 16t2 Combine like terms: 117t + -117t = 0 147 + -117t + 16t2 = 0 + -16t2 + 16t2 147 + -117t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 147 + -117t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 9.1875 + -7.3125t + t2 = 0 Move the constant term to the right: Add '-9.1875' to each side of the equation. 9.1875 + -7.3125t + -9.1875 + t2 = 0 + -9.1875 Reorder the terms: 9.1875 + -9.1875 + -7.3125t + t2 = 0 + -9.1875 Combine like terms: 9.1875 + -9.1875 = 0.0000 0.0000 + -7.3125t + t2 = 0 + -9.1875 -7.3125t + t2 = 0 + -9.1875 Combine like terms: 0 + -9.1875 = -9.1875 -7.3125t + t2 = -9.1875 The t term is -7.3125t. Take half its coefficient (-3.65625). Square it (13.36816406) and add it to both sides. Add '13.36816406' to each side of the equation. -7.3125t + 13.36816406 + t2 = -9.1875 + 13.36816406 Reorder the terms: 13.36816406 + -7.3125t + t2 = -9.1875 + 13.36816406 Combine like terms: -9.1875 + 13.36816406 = 4.18066406 13.36816406 + -7.3125t + t2 = 4.18066406 Factor a perfect square on the left side: (t + -3.65625)(t + -3.65625) = 4.18066406 Calculate the square root of the right side: 2.044667225 Break this problem into two subproblems by setting (t + -3.65625) equal to 2.044667225 and -2.044667225.Subproblem 1
t + -3.65625 = 2.044667225 Simplifying t + -3.65625 = 2.044667225 Reorder the terms: -3.65625 + t = 2.044667225 Solving -3.65625 + t = 2.044667225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = 2.044667225 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = 2.044667225 + 3.65625 t = 2.044667225 + 3.65625 Combine like terms: 2.044667225 + 3.65625 = 5.700917225 t = 5.700917225 Simplifying t = 5.700917225Subproblem 2
t + -3.65625 = -2.044667225 Simplifying t + -3.65625 = -2.044667225 Reorder the terms: -3.65625 + t = -2.044667225 Solving -3.65625 + t = -2.044667225 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.65625' to each side of the equation. -3.65625 + 3.65625 + t = -2.044667225 + 3.65625 Combine like terms: -3.65625 + 3.65625 = 0.00000 0.00000 + t = -2.044667225 + 3.65625 t = -2.044667225 + 3.65625 Combine like terms: -2.044667225 + 3.65625 = 1.611582775 t = 1.611582775 Simplifying t = 1.611582775Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.700917225, 1.611582775}
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