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Simplifying 0 = -14 + 88t + -16t2 Solving 0 = -14 + 88t + -16t2 Solving for variable 't'. Combine like terms: 0 + 14 = 14 14 + -88t + 16t2 = -14 + 88t + -16t2 + 14 + -88t + 16t2 Reorder the terms: 14 + -88t + 16t2 = -14 + 14 + 88t + -88t + -16t2 + 16t2 Combine like terms: -14 + 14 = 0 14 + -88t + 16t2 = 0 + 88t + -88t + -16t2 + 16t2 14 + -88t + 16t2 = 88t + -88t + -16t2 + 16t2 Combine like terms: 88t + -88t = 0 14 + -88t + 16t2 = 0 + -16t2 + 16t2 14 + -88t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 14 + -88t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -44t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -44t + 8t2)' equal to zero and attempt to solve: Simplifying 7 + -44t + 8t2 = 0 Solving 7 + -44t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + -5.5t + t2 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + -5.5t + -0.875 + t2 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + -5.5t + t2 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + -5.5t + t2 = 0 + -0.875 -5.5t + t2 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 -5.5t + t2 = -0.875 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 = -0.875 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = -0.875 + 7.5625 Combine like terms: -0.875 + 7.5625 = 6.6875 7.5625 + -5.5t + t2 = 6.6875 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 6.6875 Calculate the square root of the right side: 2.586020108 Break this problem into two subproblems by setting (t + -2.75) equal to 2.586020108 and -2.586020108.Subproblem 1
t + -2.75 = 2.586020108 Simplifying t + -2.75 = 2.586020108 Reorder the terms: -2.75 + t = 2.586020108 Solving -2.75 + t = 2.586020108 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 = 2.586020108 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.586020108 + 2.75 t = 2.586020108 + 2.75 Combine like terms: 2.586020108 + 2.75 = 5.336020108 t = 5.336020108 Simplifying t = 5.336020108Subproblem 2
t + -2.75 = -2.586020108 Simplifying t + -2.75 = -2.586020108 Reorder the terms: -2.75 + t = -2.586020108 Solving -2.75 + t = -2.586020108 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 = -2.586020108 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.586020108 + 2.75 t = -2.586020108 + 2.75 Combine like terms: -2.586020108 + 2.75 = 0.163979892 t = 0.163979892 Simplifying t = 0.163979892Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.336020108, 0.163979892}Solution
t = {5.336020108, 0.163979892}
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