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Simplifying 50t = -16t2 + 50 Reorder the terms: 50t = 50 + -16t2 Solving 50t = 50 + -16t2 Solving for variable 't'. Reorder the terms: -50 + 50t + 16t2 = 50 + -16t2 + -50 + 16t2 Reorder the terms: -50 + 50t + 16t2 = 50 + -50 + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -50 + 50t + 16t2 = 0 + -16t2 + 16t2 -50 + 50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -50 + 50t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-25 + 25t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + 25t + 8t2)' equal to zero and attempt to solve: Simplifying -25 + 25t + 8t2 = 0 Solving -25 + 25t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + 3.125t + t2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 3.125t + 3.125 + t2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 3.125t + t2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 3.125t + t2 = 0 + 3.125 3.125t + t2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 3.125t + t2 = 3.125 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 = 3.125 + 2.44140625 Reorder the terms: 2.44140625 + 3.125t + t2 = 3.125 + 2.44140625 Combine like terms: 3.125 + 2.44140625 = 5.56640625 2.44140625 + 3.125t + t2 = 5.56640625 Factor a perfect square on the left side: (t + 1.5625)(t + 1.5625) = 5.56640625 Calculate the square root of the right side: 2.359323261 Break this problem into two subproblems by setting (t + 1.5625) equal to 2.359323261 and -2.359323261.Subproblem 1
t + 1.5625 = 2.359323261 Simplifying t + 1.5625 = 2.359323261 Reorder the terms: 1.5625 + t = 2.359323261 Solving 1.5625 + t = 2.359323261 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 = 2.359323261 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = 2.359323261 + -1.5625 t = 2.359323261 + -1.5625 Combine like terms: 2.359323261 + -1.5625 = 0.796823261 t = 0.796823261 Simplifying t = 0.796823261Subproblem 2
t + 1.5625 = -2.359323261 Simplifying t + 1.5625 = -2.359323261 Reorder the terms: 1.5625 + t = -2.359323261 Solving 1.5625 + t = -2.359323261 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 = -2.359323261 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = -2.359323261 + -1.5625 t = -2.359323261 + -1.5625 Combine like terms: -2.359323261 + -1.5625 = -3.921823261 t = -3.921823261 Simplifying t = -3.921823261Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.796823261, -3.921823261}Solution
t = {0.796823261, -3.921823261}
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