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Simplifying 0 = -16t2 + 140t + 3 Reorder the terms: 0 = 3 + 140t + -16t2 Solving 0 = 3 + 140t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -140t + 16t2 = 3 + 140t + -16t2 + -3 + -140t + 16t2 Reorder the terms: -3 + -140t + 16t2 = 3 + -3 + 140t + -140t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -140t + 16t2 = 0 + 140t + -140t + -16t2 + 16t2 -3 + -140t + 16t2 = 140t + -140t + -16t2 + 16t2 Combine like terms: 140t + -140t = 0 -3 + -140t + 16t2 = 0 + -16t2 + 16t2 -3 + -140t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -140t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -8.75t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -8.75t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -8.75t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -8.75t + t2 = 0 + 0.1875 -8.75t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -8.75t + t2 = 0.1875 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 = 0.1875 + 19.140625 Reorder the terms: 19.140625 + -8.75t + t2 = 0.1875 + 19.140625 Combine like terms: 0.1875 + 19.140625 = 19.328125 19.140625 + -8.75t + t2 = 19.328125 Factor a perfect square on the left side: (t + -4.375)(t + -4.375) = 19.328125 Calculate the square root of the right side: 4.396376349 Break this problem into two subproblems by setting (t + -4.375) equal to 4.396376349 and -4.396376349.Subproblem 1
t + -4.375 = 4.396376349 Simplifying t + -4.375 = 4.396376349 Reorder the terms: -4.375 + t = 4.396376349 Solving -4.375 + t = 4.396376349 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 = 4.396376349 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = 4.396376349 + 4.375 t = 4.396376349 + 4.375 Combine like terms: 4.396376349 + 4.375 = 8.771376349 t = 8.771376349 Simplifying t = 8.771376349Subproblem 2
t + -4.375 = -4.396376349 Simplifying t + -4.375 = -4.396376349 Reorder the terms: -4.375 + t = -4.396376349 Solving -4.375 + t = -4.396376349 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 = -4.396376349 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + t = -4.396376349 + 4.375 t = -4.396376349 + 4.375 Combine like terms: -4.396376349 + 4.375 = -0.021376349 t = -0.021376349 Simplifying t = -0.021376349Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.771376349, -0.021376349}
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