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Simplifying 50t = -16t2 + -15 Reorder the terms: 50t = -15 + -16t2 Solving 50t = -15 + -16t2 Solving for variable 't'. Reorder the terms: 15 + 50t + 16t2 = -15 + -16t2 + 15 + 16t2 Reorder the terms: 15 + 50t + 16t2 = -15 + 15 + -16t2 + 16t2 Combine like terms: -15 + 15 = 0 15 + 50t + 16t2 = 0 + -16t2 + 16t2 15 + 50t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 15 + 50t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.9375 + 3.125t + t2 = 0 Move the constant term to the right: Add '-0.9375' to each side of the equation. 0.9375 + 3.125t + -0.9375 + t2 = 0 + -0.9375 Reorder the terms: 0.9375 + -0.9375 + 3.125t + t2 = 0 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + 3.125t + t2 = 0 + -0.9375 3.125t + t2 = 0 + -0.9375 Combine like terms: 0 + -0.9375 = -0.9375 3.125t + t2 = -0.9375 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 = -0.9375 + 2.44140625 Reorder the terms: 2.44140625 + 3.125t + t2 = -0.9375 + 2.44140625 Combine like terms: -0.9375 + 2.44140625 = 1.50390625 2.44140625 + 3.125t + t2 = 1.50390625 Factor a perfect square on the left side: (t + 1.5625)(t + 1.5625) = 1.50390625 Calculate the square root of the right side: 1.226338554 Break this problem into two subproblems by setting (t + 1.5625) equal to 1.226338554 and -1.226338554.Subproblem 1
t + 1.5625 = 1.226338554 Simplifying t + 1.5625 = 1.226338554 Reorder the terms: 1.5625 + t = 1.226338554 Solving 1.5625 + t = 1.226338554 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 = 1.226338554 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = 1.226338554 + -1.5625 t = 1.226338554 + -1.5625 Combine like terms: 1.226338554 + -1.5625 = -0.336161446 t = -0.336161446 Simplifying t = -0.336161446Subproblem 2
t + 1.5625 = -1.226338554 Simplifying t + 1.5625 = -1.226338554 Reorder the terms: 1.5625 + t = -1.226338554 Solving 1.5625 + t = -1.226338554 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 = -1.226338554 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = -1.226338554 + -1.5625 t = -1.226338554 + -1.5625 Combine like terms: -1.226338554 + -1.5625 = -2.788838554 t = -2.788838554 Simplifying t = -2.788838554Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.336161446, -2.788838554}
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