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Simplifying 8t2 + -70t + -85 = 0 Reorder the terms: -85 + -70t + 8t2 = 0 Solving -85 + -70t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -10.625 + -8.75t + t2 = 0 Move the constant term to the right: Add '10.625' to each side of the equation. -10.625 + -8.75t + 10.625 + t2 = 0 + 10.625 Reorder the terms: -10.625 + 10.625 + -8.75t + t2 = 0 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + -8.75t + t2 = 0 + 10.625 -8.75t + t2 = 0 + 10.625 Combine like terms: 0 + 10.625 = 10.625 -8.75t + t2 = 10.625 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 = 10.625 + 19.140625 Reorder the terms: 19.140625 + -8.75t + t2 = 10.625 + 19.140625 Combine like terms: 10.625 + 19.140625 = 29.765625 19.140625 + -8.75t + t2 = 29.765625 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 29.765625 Calculate the square root of the right side: 5.455788211 Break this problem into two subproblems by setting (t + -4.375) equal to 5.455788211 and -5.455788211.Subproblem 1
t + -4.375 = 5.455788211 Simplifying t + -4.375 = 5.455788211 Reorder the terms: -4.375 + t = 5.455788211 Solving -4.375 + t = 5.455788211 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 = 5.455788211 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 5.455788211 + 4.375 t = 5.455788211 + 4.375 Combine like terms: 5.455788211 + 4.375 = 9.830788211 t = 9.830788211 Simplifying t = 9.830788211Subproblem 2
t + -4.375 = -5.455788211 Simplifying t + -4.375 = -5.455788211 Reorder the terms: -4.375 + t = -5.455788211 Solving -4.375 + t = -5.455788211 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 = -5.455788211 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -5.455788211 + 4.375 t = -5.455788211 + 4.375 Combine like terms: -5.455788211 + 4.375 = -1.080788211 t = -1.080788211 Simplifying t = -1.080788211Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.830788211, -1.080788211}
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