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Simplifying 0 = -16t2 + -10t + 1250 Reorder the terms: 0 = 1250 + -10t + -16t2 Solving 0 = 1250 + -10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1250 = -1250 -1250 + 10t + 16t2 = 1250 + -10t + -16t2 + -1250 + 10t + 16t2 Reorder the terms: -1250 + 10t + 16t2 = 1250 + -1250 + -10t + 10t + -16t2 + 16t2 Combine like terms: 1250 + -1250 = 0 -1250 + 10t + 16t2 = 0 + -10t + 10t + -16t2 + 16t2 -1250 + 10t + 16t2 = -10t + 10t + -16t2 + 16t2 Combine like terms: -10t + 10t = 0 -1250 + 10t + 16t2 = 0 + -16t2 + 16t2 -1250 + 10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1250 + 10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-625 + 5t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-625 + 5t + 8t2)' equal to zero and attempt to solve: Simplifying -625 + 5t + 8t2 = 0 Solving -625 + 5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -78.125 + 0.625t + t2 = 0 Move the constant term to the right: Add '78.125' to each side of the equation. -78.125 + 0.625t + 78.125 + t2 = 0 + 78.125 Reorder the terms: -78.125 + 78.125 + 0.625t + t2 = 0 + 78.125 Combine like terms: -78.125 + 78.125 = 0.000 0.000 + 0.625t + t2 = 0 + 78.125 0.625t + t2 = 0 + 78.125 Combine like terms: 0 + 78.125 = 78.125 0.625t + t2 = 78.125 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 78.125 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 78.125 + 0.09765625 Combine like terms: 78.125 + 0.09765625 = 78.22265625 0.09765625 + 0.625t + t2 = 78.22265625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 78.22265625 Calculate the square root of the right side: 8.844357311 Break this problem into two subproblems by setting (t + 0.3125) equal to 8.844357311 and -8.844357311.Subproblem 1
t + 0.3125 = 8.844357311 Simplifying t + 0.3125 = 8.844357311 Reorder the terms: 0.3125 + t = 8.844357311 Solving 0.3125 + t = 8.844357311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 8.844357311 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 8.844357311 + -0.3125 t = 8.844357311 + -0.3125 Combine like terms: 8.844357311 + -0.3125 = 8.531857311 t = 8.531857311 Simplifying t = 8.531857311Subproblem 2
t + 0.3125 = -8.844357311 Simplifying t + 0.3125 = -8.844357311 Reorder the terms: 0.3125 + t = -8.844357311 Solving 0.3125 + t = -8.844357311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -8.844357311 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -8.844357311 + -0.3125 t = -8.844357311 + -0.3125 Combine like terms: -8.844357311 + -0.3125 = -9.156857311 t = -9.156857311 Simplifying t = -9.156857311Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.531857311, -9.156857311}Solution
t = {8.531857311, -9.156857311}
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