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Simplifying 28 = -16t2 + 50t Reorder the terms: 28 = 50t + -16t2 Solving 28 = 50t + -16t2 Solving for variable 't'. Reorder the terms: 28 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 28 + -50t + 16t2 = 0 + -16t2 + 16t2 28 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 28 + -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -25t + 8t2)' equal to zero and attempt to solve: Simplifying 14 + -25t + 8t2 = 0 Solving 14 + -25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.75 + -3.125t + t2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -3.125t + -1.75 + t2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -3.125t + t2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -3.125t + t2 = 0 + -1.75 -3.125t + t2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -3.125t + t2 = -1.75 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = -1.75 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = -1.75 + 2.44140625 Combine like terms: -1.75 + 2.44140625 = 0.69140625 2.44140625 + -3.125t + t2 = 0.69140625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (t + -1.5625) equal to 0.831508418 and -0.831508418.Subproblem 1
t + -1.5625 = 0.831508418 Simplifying t + -1.5625 = 0.831508418 Reorder the terms: -1.5625 + t = 0.831508418 Solving -1.5625 + t = 0.831508418 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 0.831508418 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 0.831508418 + 1.5625 t = 0.831508418 + 1.5625 Combine like terms: 0.831508418 + 1.5625 = 2.394008418 t = 2.394008418 Simplifying t = 2.394008418Subproblem 2
t + -1.5625 = -0.831508418 Simplifying t + -1.5625 = -0.831508418 Reorder the terms: -1.5625 + t = -0.831508418 Solving -1.5625 + t = -0.831508418 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -0.831508418 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -0.831508418 + 1.5625 t = -0.831508418 + 1.5625 Combine like terms: -0.831508418 + 1.5625 = 0.730991582 t = 0.730991582 Simplifying t = 0.730991582Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.394008418, 0.730991582}Solution
t = {2.394008418, 0.730991582}
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