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Simplifying 16t2 + -140t = 68 Reorder the terms: -140t + 16t2 = 68 Solving -140t + 16t2 = 68 Solving for variable 't'. Reorder the terms: -68 + -140t + 16t2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + -140t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-17 + -35t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-17 + -35t + 4t2)' equal to zero and attempt to solve: Simplifying -17 + -35t + 4t2 = 0 Solving -17 + -35t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -8.75t + t2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -8.75t + 4.25 + t2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -8.75t + t2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -8.75t + t2 = 0 + 4.25 -8.75t + t2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -8.75t + t2 = 4.25 The t term is -8.75t. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75t + 19.140625 + t2 = 4.25 + 19.140625 Reorder the terms: 19.140625 + -8.75t + t2 = 4.25 + 19.140625 Combine like terms: 4.25 + 19.140625 = 23.390625 19.140625 + -8.75t + t2 = 23.390625 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 23.390625 Calculate the square root of the right side: 4.836385531 Break this problem into two subproblems by setting (t + -4.375) equal to 4.836385531 and -4.836385531.Subproblem 1
t + -4.375 = 4.836385531 Simplifying t + -4.375 = 4.836385531 Reorder the terms: -4.375 + t = 4.836385531 Solving -4.375 + t = 4.836385531 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = 4.836385531 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 4.836385531 + 4.375 t = 4.836385531 + 4.375 Combine like terms: 4.836385531 + 4.375 = 9.211385531 t = 9.211385531 Simplifying t = 9.211385531Subproblem 2
t + -4.375 = -4.836385531 Simplifying t + -4.375 = -4.836385531 Reorder the terms: -4.375 + t = -4.836385531 Solving -4.375 + t = -4.836385531 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + t = -4.836385531 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -4.836385531 + 4.375 t = -4.836385531 + 4.375 Combine like terms: -4.836385531 + 4.375 = -0.461385531 t = -0.461385531 Simplifying t = -0.461385531Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.211385531, -0.461385531}Solution
t = {9.211385531, -0.461385531}
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