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Simplifying -16t2 + 50t + 1250 = 0 Reorder the terms: 1250 + 50t + -16t2 = 0 Solving 1250 + 50t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(625 + 25t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(625 + 25t + -8t2)' equal to zero and attempt to solve: Simplifying 625 + 25t + -8t2 = 0 Solving 625 + 25t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -78.125 + -3.125t + t2 = 0 Move the constant term to the right: Add '78.125' to each side of the equation. -78.125 + -3.125t + 78.125 + t2 = 0 + 78.125 Reorder the terms: -78.125 + 78.125 + -3.125t + t2 = 0 + 78.125 Combine like terms: -78.125 + 78.125 = 0.000 0.000 + -3.125t + t2 = 0 + 78.125 -3.125t + t2 = 0 + 78.125 Combine like terms: 0 + 78.125 = 78.125 -3.125t + t2 = 78.125 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 = 78.125 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = 78.125 + 2.44140625 Combine like terms: 78.125 + 2.44140625 = 80.56640625 2.44140625 + -3.125t + t2 = 80.56640625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 80.56640625 Calculate the square root of the right side: 8.975879135 Break this problem into two subproblems by setting (t + -1.5625) equal to 8.975879135 and -8.975879135.Subproblem 1
t + -1.5625 = 8.975879135 Simplifying t + -1.5625 = 8.975879135 Reorder the terms: -1.5625 + t = 8.975879135 Solving -1.5625 + t = 8.975879135 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 = 8.975879135 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 8.975879135 + 1.5625 t = 8.975879135 + 1.5625 Combine like terms: 8.975879135 + 1.5625 = 10.538379135 t = 10.538379135 Simplifying t = 10.538379135Subproblem 2
t + -1.5625 = -8.975879135 Simplifying t + -1.5625 = -8.975879135 Reorder the terms: -1.5625 + t = -8.975879135 Solving -1.5625 + t = -8.975879135 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 = -8.975879135 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -8.975879135 + 1.5625 t = -8.975879135 + 1.5625 Combine like terms: -8.975879135 + 1.5625 = -7.413379135 t = -7.413379135 Simplifying t = -7.413379135Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.538379135, -7.413379135}Solution
t = {10.538379135, -7.413379135}
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