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Simplifying 141.015625 = -16t2 + 95t Reorder the terms: 141.015625 = 95t + -16t2 Solving 141.015625 = 95t + -16t2 Solving for variable 't'. Reorder the terms: 141.015625 + -95t + 16t2 = 95t + -95t + -16t2 + 16t2 Combine like terms: 95t + -95t = 0 141.015625 + -95t + 16t2 = 0 + -16t2 + 16t2 141.015625 + -95t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 141.015625 + -95t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 8.813476563 + -5.9375t + t2 = 0 Move the constant term to the right: Add '-8.813476563' to each side of the equation. 8.813476563 + -5.9375t + -8.813476563 + t2 = 0 + -8.813476563 Reorder the terms: 8.813476563 + -8.813476563 + -5.9375t + t2 = 0 + -8.813476563 Combine like terms: 8.813476563 + -8.813476563 = 0.000000000 0.000000000 + -5.9375t + t2 = 0 + -8.813476563 -5.9375t + t2 = 0 + -8.813476563 Combine like terms: 0 + -8.813476563 = -8.813476563 -5.9375t + t2 = -8.813476563 The t term is -5.9375t. Take half its coefficient (-2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. -5.9375t + 8.813476563 + t2 = -8.813476563 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375t + t2 = -8.813476563 + 8.813476563 Combine like terms: -8.813476563 + 8.813476563 = 0.000000000 8.813476563 + -5.9375t + t2 = 0.000000000 Factor a perfect square on the left side: (t + -2.96875)(t + -2.96875) = 0.000000000 Calculate the square root of the right side: 0.000000000 Break this problem into two subproblems by setting (t + -2.96875) equal to 0.000000000 and 0.000000000.Subproblem 1
t + -2.96875 = 0.000000000 Simplifying t + -2.96875 = 0.000000000 Reorder the terms: -2.96875 + t = 0.000000000 Solving -2.96875 + t = 0.000000000 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + t = 0.000000000 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = 0.000000000 + 2.96875 t = 0.000000000 + 2.96875 Combine like terms: 0.000000000 + 2.96875 = 2.96875 t = 2.96875 Simplifying t = 2.96875Subproblem 2
t + -2.96875 = 0.000000000 Simplifying t + -2.96875 = 0.000000000 Reorder the terms: -2.96875 + t = 0.000000000 Solving -2.96875 + t = 0.000000000 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + t = 0.000000000 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = 0.000000000 + 2.96875 t = 0.000000000 + 2.96875 Combine like terms: 0.000000000 + 2.96875 = 2.96875 t = 2.96875 Simplifying t = 2.96875Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.96875, 2.96875}
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