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Simplifying 114 = -16t2 + 95t + 0 Reorder the terms: 114 = 0 + 95t + -16t2 Remove the zero: 114 = 95t + -16t2 Solving 114 = 95t + -16t2 Solving for variable 't'. Reorder the terms: 114 + -95t + 16t2 = 95t + -95t + -16t2 + 16t2 Combine like terms: 95t + -95t = 0 114 + -95t + 16t2 = 0 + -16t2 + 16t2 114 + -95t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 114 + -95t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 7.125 + -5.9375t + t2 = 0 Move the constant term to the right: Add '-7.125' to each side of the equation. 7.125 + -5.9375t + -7.125 + t2 = 0 + -7.125 Reorder the terms: 7.125 + -7.125 + -5.9375t + t2 = 0 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + -5.9375t + t2 = 0 + -7.125 -5.9375t + t2 = 0 + -7.125 Combine like terms: 0 + -7.125 = -7.125 -5.9375t + t2 = -7.125 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 = -7.125 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375t + t2 = -7.125 + 8.813476563 Combine like terms: -7.125 + 8.813476563 = 1.688476563 8.813476563 + -5.9375t + t2 = 1.688476563 Factor a perfect square on the left side: (t + -2.96875)(t + -2.96875) = 1.688476563 Calculate the square root of the right side: 1.299413931 Break this problem into two subproblems by setting (t + -2.96875) equal to 1.299413931 and -1.299413931.Subproblem 1
t + -2.96875 = 1.299413931 Simplifying t + -2.96875 = 1.299413931 Reorder the terms: -2.96875 + t = 1.299413931 Solving -2.96875 + t = 1.299413931 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 = 1.299413931 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = 1.299413931 + 2.96875 t = 1.299413931 + 2.96875 Combine like terms: 1.299413931 + 2.96875 = 4.268163931 t = 4.268163931 Simplifying t = 4.268163931Subproblem 2
t + -2.96875 = -1.299413931 Simplifying t + -2.96875 = -1.299413931 Reorder the terms: -2.96875 + t = -1.299413931 Solving -2.96875 + t = -1.299413931 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 = -1.299413931 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + t = -1.299413931 + 2.96875 t = -1.299413931 + 2.96875 Combine like terms: -1.299413931 + 2.96875 = 1.669336069 t = 1.669336069 Simplifying t = 1.669336069Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.268163931, 1.669336069}
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