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Simplifying t = -16t2 + -16t + 60 Reorder the terms: t = 60 + -16t + -16t2 Solving t = 60 + -16t + -16t2 Solving for variable 't'. Reorder the terms: -60 + t + 16t + 16t2 = 60 + -16t + -16t2 + -60 + 16t + 16t2 Combine like terms: t + 16t = 17t -60 + 17t + 16t2 = 60 + -16t + -16t2 + -60 + 16t + 16t2 Reorder the terms: -60 + 17t + 16t2 = 60 + -60 + -16t + 16t + -16t2 + 16t2 Combine like terms: 60 + -60 = 0 -60 + 17t + 16t2 = 0 + -16t + 16t + -16t2 + 16t2 -60 + 17t + 16t2 = -16t + 16t + -16t2 + 16t2 Combine like terms: -16t + 16t = 0 -60 + 17t + 16t2 = 0 + -16t2 + 16t2 -60 + 17t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -60 + 17t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.75 + 1.0625t + t2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 1.0625t + 3.75 + t2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 1.0625t + t2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 1.0625t + t2 = 0 + 3.75 1.0625t + t2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 1.0625t + t2 = 3.75 The t term is 1.0625t. Take half its coefficient (0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. 1.0625t + 0.2822265625 + t2 = 3.75 + 0.2822265625 Reorder the terms: 0.2822265625 + 1.0625t + t2 = 3.75 + 0.2822265625 Combine like terms: 3.75 + 0.2822265625 = 4.0322265625 0.2822265625 + 1.0625t + t2 = 4.0322265625 Factor a perfect square on the left side: (t + 0.53125)(t + 0.53125) = 4.0322265625 Calculate the square root of the right side: 2.008040478 Break this problem into two subproblems by setting (t + 0.53125) equal to 2.008040478 and -2.008040478.Subproblem 1
t + 0.53125 = 2.008040478 Simplifying t + 0.53125 = 2.008040478 Reorder the terms: 0.53125 + t = 2.008040478 Solving 0.53125 + t = 2.008040478 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + t = 2.008040478 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + t = 2.008040478 + -0.53125 t = 2.008040478 + -0.53125 Combine like terms: 2.008040478 + -0.53125 = 1.476790478 t = 1.476790478 Simplifying t = 1.476790478Subproblem 2
t + 0.53125 = -2.008040478 Simplifying t + 0.53125 = -2.008040478 Reorder the terms: 0.53125 + t = -2.008040478 Solving 0.53125 + t = -2.008040478 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + t = -2.008040478 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + t = -2.008040478 + -0.53125 t = -2.008040478 + -0.53125 Combine like terms: -2.008040478 + -0.53125 = -2.539290478 t = -2.539290478 Simplifying t = -2.539290478Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.476790478, -2.539290478}
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