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Simplifying 0 = -16t2 + -7t + 35 Reorder the terms: 0 = 35 + -7t + -16t2 Solving 0 = 35 + -7t + -16t2 Solving for variable 't'. Combine like terms: 0 + -35 = -35 -35 + 7t + 16t2 = 35 + -7t + -16t2 + -35 + 7t + 16t2 Reorder the terms: -35 + 7t + 16t2 = 35 + -35 + -7t + 7t + -16t2 + 16t2 Combine like terms: 35 + -35 = 0 -35 + 7t + 16t2 = 0 + -7t + 7t + -16t2 + 16t2 -35 + 7t + 16t2 = -7t + 7t + -16t2 + 16t2 Combine like terms: -7t + 7t = 0 -35 + 7t + 16t2 = 0 + -16t2 + 16t2 -35 + 7t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -35 + 7t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.1875 + 0.4375t + t2 = 0 Move the constant term to the right: Add '2.1875' to each side of the equation. -2.1875 + 0.4375t + 2.1875 + t2 = 0 + 2.1875 Reorder the terms: -2.1875 + 2.1875 + 0.4375t + t2 = 0 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + 0.4375t + t2 = 0 + 2.1875 0.4375t + t2 = 0 + 2.1875 Combine like terms: 0 + 2.1875 = 2.1875 0.4375t + t2 = 2.1875 The t term is 0.4375t. Take half its coefficient (0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. 0.4375t + 0.0478515625 + t2 = 2.1875 + 0.0478515625 Reorder the terms: 0.0478515625 + 0.4375t + t2 = 2.1875 + 0.0478515625 Combine like terms: 2.1875 + 0.0478515625 = 2.2353515625 0.0478515625 + 0.4375t + t2 = 2.2353515625 Factor a perfect square on the left side: (t + 0.21875)(t + 0.21875) = 2.2353515625 Calculate the square root of the right side: 1.495109214 Break this problem into two subproblems by setting (t + 0.21875) equal to 1.495109214 and -1.495109214.Subproblem 1
t + 0.21875 = 1.495109214 Simplifying t + 0.21875 = 1.495109214 Reorder the terms: 0.21875 + t = 1.495109214 Solving 0.21875 + t = 1.495109214 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + t = 1.495109214 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + t = 1.495109214 + -0.21875 t = 1.495109214 + -0.21875 Combine like terms: 1.495109214 + -0.21875 = 1.276359214 t = 1.276359214 Simplifying t = 1.276359214Subproblem 2
t + 0.21875 = -1.495109214 Simplifying t + 0.21875 = -1.495109214 Reorder the terms: 0.21875 + t = -1.495109214 Solving 0.21875 + t = -1.495109214 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + t = -1.495109214 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + t = -1.495109214 + -0.21875 t = -1.495109214 + -0.21875 Combine like terms: -1.495109214 + -0.21875 = -1.713859214 t = -1.713859214 Simplifying t = -1.713859214Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.276359214, -1.713859214}
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