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Simplifying -100 = -16t2 + 50t Reorder the terms: -100 = 50t + -16t2 Solving -100 = 50t + -16t2 Solving for variable 't'. Reorder the terms: -100 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 -100 + -50t + 16t2 = 0 + -16t2 + 16t2 -100 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + -25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + -25t + 8t2)' equal to zero and attempt to solve: Simplifying -50 + -25t + 8t2 = 0 Solving -50 + -25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.25 + -3.125t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -3.125t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -3.125t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -3.125t + t2 = 0 + 6.25 -3.125t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -3.125t + t2 = 6.25 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 = 6.25 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 6.25 + 2.44140625 Combine like terms: 6.25 + 2.44140625 = 8.69140625 2.44140625 + -3.125t + t2 = 8.69140625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 8.69140625 Calculate the square root of the right side: 2.948119104 Break this problem into two subproblems by setting (t + -1.5625) equal to 2.948119104 and -2.948119104.Subproblem 1
t + -1.5625 = 2.948119104 Simplifying t + -1.5625 = 2.948119104 Reorder the terms: -1.5625 + t = 2.948119104 Solving -1.5625 + t = 2.948119104 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 = 2.948119104 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 2.948119104 + 1.5625 t = 2.948119104 + 1.5625 Combine like terms: 2.948119104 + 1.5625 = 4.510619104 t = 4.510619104 Simplifying t = 4.510619104Subproblem 2
t + -1.5625 = -2.948119104 Simplifying t + -1.5625 = -2.948119104 Reorder the terms: -1.5625 + t = -2.948119104 Solving -1.5625 + t = -2.948119104 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 = -2.948119104 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -2.948119104 + 1.5625 t = -2.948119104 + 1.5625 Combine like terms: -2.948119104 + 1.5625 = -1.385619104 t = -1.385619104 Simplifying t = -1.385619104Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.510619104, -1.385619104}Solution
t = {4.510619104, -1.385619104}
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