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Simplifying 0 = -16t2 + 88t + 5 Reorder the terms: 0 = 5 + 88t + -16t2 Solving 0 = 5 + 88t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -88t + 16t2 = 5 + 88t + -16t2 + -5 + -88t + 16t2 Reorder the terms: -5 + -88t + 16t2 = 5 + -5 + 88t + -88t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + -88t + 16t2 = 0 + 88t + -88t + -16t2 + 16t2 -5 + -88t + 16t2 = 88t + -88t + -16t2 + 16t2 Combine like terms: 88t + -88t = 0 -5 + -88t + 16t2 = 0 + -16t2 + 16t2 -5 + -88t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -88t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -5.5t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -5.5t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -5.5t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -5.5t + t2 = 0 + 0.3125 -5.5t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -5.5t + t2 = 0.3125 The t term is -5.5t. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t + 7.5625 + t2 = 0.3125 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = 0.3125 + 7.5625 Combine like terms: 0.3125 + 7.5625 = 7.875 7.5625 + -5.5t + t2 = 7.875 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 7.875 Calculate the square root of the right side: 2.80624304 Break this problem into two subproblems by setting (t + -2.75) equal to 2.80624304 and -2.80624304.Subproblem 1
t + -2.75 = 2.80624304 Simplifying t + -2.75 = 2.80624304 Reorder the terms: -2.75 + t = 2.80624304 Solving -2.75 + t = 2.80624304 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = 2.80624304 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.80624304 + 2.75 t = 2.80624304 + 2.75 Combine like terms: 2.80624304 + 2.75 = 5.55624304 t = 5.55624304 Simplifying t = 5.55624304Subproblem 2
t + -2.75 = -2.80624304 Simplifying t + -2.75 = -2.80624304 Reorder the terms: -2.75 + t = -2.80624304 Solving -2.75 + t = -2.80624304 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = -2.80624304 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.80624304 + 2.75 t = -2.80624304 + 2.75 Combine like terms: -2.80624304 + 2.75 = -0.05624304 t = -0.05624304 Simplifying t = -0.05624304Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.55624304, -0.05624304}
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