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Simplifying 40 = 5 + 50t + -16t2 Solving 40 = 5 + 50t + -16t2 Solving for variable 't'. Combine like terms: 40 + -5 = 35 35 + -50t + 16t2 = 5 + 50t + -16t2 + -5 + -50t + 16t2 Reorder the terms: 35 + -50t + 16t2 = 5 + -5 + 50t + -50t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 35 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2 35 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2 Combine like terms: 50t + -50t = 0 35 + -50t + 16t2 = 0 + -16t2 + 16t2 35 + -50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 35 + -50t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.1875 + -3.125t + t2 = 0 Move the constant term to the right: Add '-2.1875' to each side of the equation. 2.1875 + -3.125t + -2.1875 + t2 = 0 + -2.1875 Reorder the terms: 2.1875 + -2.1875 + -3.125t + t2 = 0 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + -3.125t + t2 = 0 + -2.1875 -3.125t + t2 = 0 + -2.1875 Combine like terms: 0 + -2.1875 = -2.1875 -3.125t + t2 = -2.1875 The t term is -3.125t. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125t + 2.44140625 + t2 = -2.1875 + 2.44140625 Reorder the terms: 2.44140625 + -3.125t + t2 = -2.1875 + 2.44140625 Combine like terms: -2.1875 + 2.44140625 = 0.25390625 2.44140625 + -3.125t + t2 = 0.25390625 Factor a perfect square on the left side: (t + -1.5625)(t + -1.5625) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (t + -1.5625) equal to 0.503891109 and -0.503891109.Subproblem 1
t + -1.5625 = 0.503891109 Simplifying t + -1.5625 = 0.503891109 Reorder the terms: -1.5625 + t = 0.503891109 Solving -1.5625 + t = 0.503891109 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = 0.503891109 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = 0.503891109 + 1.5625 t = 0.503891109 + 1.5625 Combine like terms: 0.503891109 + 1.5625 = 2.066391109 t = 2.066391109 Simplifying t = 2.066391109Subproblem 2
t + -1.5625 = -0.503891109 Simplifying t + -1.5625 = -0.503891109 Reorder the terms: -1.5625 + t = -0.503891109 Solving -1.5625 + t = -0.503891109 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + t = -0.503891109 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + t = -0.503891109 + 1.5625 t = -0.503891109 + 1.5625 Combine like terms: -0.503891109 + 1.5625 = 1.058608891 t = 1.058608891 Simplifying t = 1.058608891Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.066391109, 1.058608891}
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