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Simplifying -16t2 + 140t + 37 = 0 Reorder the terms: 37 + 140t + -16t2 = 0 Solving 37 + 140t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.3125 + -8.75t + t2 = 0 Move the constant term to the right: Add '2.3125' to each side of the equation. -2.3125 + -8.75t + 2.3125 + t2 = 0 + 2.3125 Reorder the terms: -2.3125 + 2.3125 + -8.75t + t2 = 0 + 2.3125 Combine like terms: -2.3125 + 2.3125 = 0.0000 0.0000 + -8.75t + t2 = 0 + 2.3125 -8.75t + t2 = 0 + 2.3125 Combine like terms: 0 + 2.3125 = 2.3125 -8.75t + t2 = 2.3125 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 = 2.3125 + 19.140625 Reorder the terms: 19.140625 + -8.75t + t2 = 2.3125 + 19.140625 Combine like terms: 2.3125 + 19.140625 = 21.453125 19.140625 + -8.75t + t2 = 21.453125 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 21.453125 Calculate the square root of the right side: 4.631751828 Break this problem into two subproblems by setting (t + -4.375) equal to 4.631751828 and -4.631751828.Subproblem 1
t + -4.375 = 4.631751828 Simplifying t + -4.375 = 4.631751828 Reorder the terms: -4.375 + t = 4.631751828 Solving -4.375 + t = 4.631751828 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 = 4.631751828 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 4.631751828 + 4.375 t = 4.631751828 + 4.375 Combine like terms: 4.631751828 + 4.375 = 9.006751828 t = 9.006751828 Simplifying t = 9.006751828Subproblem 2
t + -4.375 = -4.631751828 Simplifying t + -4.375 = -4.631751828 Reorder the terms: -4.375 + t = -4.631751828 Solving -4.375 + t = -4.631751828 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 = -4.631751828 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -4.631751828 + 4.375 t = -4.631751828 + 4.375 Combine like terms: -4.631751828 + 4.375 = -0.256751828 t = -0.256751828 Simplifying t = -0.256751828Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.006751828, -0.256751828}
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