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Simplifying 0 = 140t + -16t2 + -68 Reorder the terms: 0 = -68 + 140t + -16t2 Solving 0 = -68 + 140t + -16t2 Solving for variable 't'. Combine like terms: 0 + 68 = 68 68 + -140t + 16t2 = -68 + 140t + -16t2 + 68 + -140t + 16t2 Reorder the terms: 68 + -140t + 16t2 = -68 + 68 + 140t + -140t + -16t2 + 16t2 Combine like terms: -68 + 68 = 0 68 + -140t + 16t2 = 0 + 140t + -140t + -16t2 + 16t2 68 + -140t + 16t2 = 140t + -140t + -16t2 + 16t2 Combine like terms: 140t + -140t = 0 68 + -140t + 16t2 = 0 + -16t2 + 16t2 68 + -140t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 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 = 14.890625 19.140625 + -8.75t + t2 = 14.890625 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 14.890625 Calculate the square root of the right side: 3.85883726 Break this problem into two subproblems by setting (t + -4.375) equal to 3.85883726 and -3.85883726.Subproblem 1
t + -4.375 = 3.85883726 Simplifying t + -4.375 = 3.85883726 Reorder the terms: -4.375 + t = 3.85883726 Solving -4.375 + t = 3.85883726 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 = 3.85883726 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 3.85883726 + 4.375 t = 3.85883726 + 4.375 Combine like terms: 3.85883726 + 4.375 = 8.23383726 t = 8.23383726 Simplifying t = 8.23383726Subproblem 2
t + -4.375 = -3.85883726 Simplifying t + -4.375 = -3.85883726 Reorder the terms: -4.375 + t = -3.85883726 Solving -4.375 + t = -3.85883726 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 = -3.85883726 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -3.85883726 + 4.375 t = -3.85883726 + 4.375 Combine like terms: -3.85883726 + 4.375 = 0.51616274 t = 0.51616274 Simplifying t = 0.51616274Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.23383726, 0.51616274}Solution
t = {8.23383726, 0.51616274}
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