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Simplifying 82 = 202t + -16t2 Solving 82 = 202t + -16t2 Solving for variable 't'. Reorder the terms: 82 + -202t + 16t2 = 202t + -202t + -16t2 + 16t2 Combine like terms: 202t + -202t = 0 82 + -202t + 16t2 = 0 + -16t2 + 16t2 82 + -202t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 82 + -202t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(41 + -101t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(41 + -101t + 8t2)' equal to zero and attempt to solve: Simplifying 41 + -101t + 8t2 = 0 Solving 41 + -101t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 5.125 + -12.625t + t2 = 0 Move the constant term to the right: Add '-5.125' to each side of the equation. 5.125 + -12.625t + -5.125 + t2 = 0 + -5.125 Reorder the terms: 5.125 + -5.125 + -12.625t + t2 = 0 + -5.125 Combine like terms: 5.125 + -5.125 = 0.000 0.000 + -12.625t + t2 = 0 + -5.125 -12.625t + t2 = 0 + -5.125 Combine like terms: 0 + -5.125 = -5.125 -12.625t + t2 = -5.125 The t term is -12.625t. Take half its coefficient (-6.3125). Square it (39.84765625) and add it to both sides. Add '39.84765625' to each side of the equation. -12.625t + 39.84765625 + t2 = -5.125 + 39.84765625 Reorder the terms: 39.84765625 + -12.625t + t2 = -5.125 + 39.84765625 Combine like terms: -5.125 + 39.84765625 = 34.72265625 39.84765625 + -12.625t + t2 = 34.72265625 Factor a perfect square on the left side: (t + -6.3125)(t + -6.3125) = 34.72265625 Calculate the square root of the right side: 5.892593338 Break this problem into two subproblems by setting (t + -6.3125) equal to 5.892593338 and -5.892593338.Subproblem 1
t + -6.3125 = 5.892593338 Simplifying t + -6.3125 = 5.892593338 Reorder the terms: -6.3125 + t = 5.892593338 Solving -6.3125 + t = 5.892593338 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.3125' to each side of the equation. -6.3125 + 6.3125 + t = 5.892593338 + 6.3125 Combine like terms: -6.3125 + 6.3125 = 0.0000 0.0000 + t = 5.892593338 + 6.3125 t = 5.892593338 + 6.3125 Combine like terms: 5.892593338 + 6.3125 = 12.205093338 t = 12.205093338 Simplifying t = 12.205093338Subproblem 2
t + -6.3125 = -5.892593338 Simplifying t + -6.3125 = -5.892593338 Reorder the terms: -6.3125 + t = -5.892593338 Solving -6.3125 + t = -5.892593338 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.3125' to each side of the equation. -6.3125 + 6.3125 + t = -5.892593338 + 6.3125 Combine like terms: -6.3125 + 6.3125 = 0.0000 0.0000 + t = -5.892593338 + 6.3125 t = -5.892593338 + 6.3125 Combine like terms: -5.892593338 + 6.3125 = 0.419906662 t = 0.419906662 Simplifying t = 0.419906662Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.205093338, 0.419906662}Solution
t = {12.205093338, 0.419906662}
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