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Simplifying 0 = -16t2 + 95t + 144 Reorder the terms: 0 = 144 + 95t + -16t2 Solving 0 = 144 + 95t + -16t2 Solving for variable 't'. Combine like terms: 0 + -144 = -144 -144 + -95t + 16t2 = 144 + 95t + -16t2 + -144 + -95t + 16t2 Reorder the terms: -144 + -95t + 16t2 = 144 + -144 + 95t + -95t + -16t2 + 16t2 Combine like terms: 144 + -144 = 0 -144 + -95t + 16t2 = 0 + 95t + -95t + -16t2 + 16t2 -144 + -95t + 16t2 = 95t + -95t + -16t2 + 16t2 Combine like terms: 95t + -95t = 0 -144 + -95t + 16t2 = 0 + -16t2 + 16t2 -144 + -95t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -144 + -95t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -9 + -5.9375t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -5.9375t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -5.9375t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5.9375t + t2 = 0 + 9 -5.9375t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -5.9375t + t2 = 9 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 = 9 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375t + t2 = 9 + 8.813476563 Combine like terms: 9 + 8.813476563 = 17.813476563 8.813476563 + -5.9375t + t2 = 17.813476563 Factor a perfect square on the left side: (t + -2.96875)(t + -2.96875) = 17.813476563 Calculate the square root of the right side: 4.220601446 Break this problem into two subproblems by setting (t + -2.96875) equal to 4.220601446 and -4.220601446.Subproblem 1
t + -2.96875 = 4.220601446 Simplifying t + -2.96875 = 4.220601446 Reorder the terms: -2.96875 + t = 4.220601446 Solving -2.96875 + t = 4.220601446 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 = 4.220601446 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = 4.220601446 + 2.96875 t = 4.220601446 + 2.96875 Combine like terms: 4.220601446 + 2.96875 = 7.189351446 t = 7.189351446 Simplifying t = 7.189351446Subproblem 2
t + -2.96875 = -4.220601446 Simplifying t + -2.96875 = -4.220601446 Reorder the terms: -2.96875 + t = -4.220601446 Solving -2.96875 + t = -4.220601446 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 = -4.220601446 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = -4.220601446 + 2.96875 t = -4.220601446 + 2.96875 Combine like terms: -4.220601446 + 2.96875 = -1.251851446 t = -1.251851446 Simplifying t = -1.251851446Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.189351446, -1.251851446}
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