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Simplifying 0 = 16t2 + 50t + 3.5 Reorder the terms: 0 = 3.5 + 50t + 16t2 Solving 0 = 3.5 + 50t + 16t2 Solving for variable 't'. Combine like terms: 0 + -3.5 = -3.5 -3.5 + -50t + -16t2 = 3.5 + 50t + 16t2 + -3.5 + -50t + -16t2 Reorder the terms: -3.5 + -50t + -16t2 = 3.5 + -3.5 + 50t + -50t + 16t2 + -16t2 Combine like terms: 3.5 + -3.5 = 0.0 -3.5 + -50t + -16t2 = 0.0 + 50t + -50t + 16t2 + -16t2 -3.5 + -50t + -16t2 = 50t + -50t + 16t2 + -16t2 Combine like terms: 50t + -50t = 0 -3.5 + -50t + -16t2 = 0 + 16t2 + -16t2 -3.5 + -50t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -3.5 + -50t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.21875 + 3.125t + t2 = 0 Move the constant term to the right: Add '-0.21875' to each side of the equation. 0.21875 + 3.125t + -0.21875 + t2 = 0 + -0.21875 Reorder the terms: 0.21875 + -0.21875 + 3.125t + t2 = 0 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + 3.125t + t2 = 0 + -0.21875 3.125t + t2 = 0 + -0.21875 Combine like terms: 0 + -0.21875 = -0.21875 3.125t + t2 = -0.21875 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 = -0.21875 + 2.44140625 Reorder the terms: 2.44140625 + 3.125t + t2 = -0.21875 + 2.44140625 Combine like terms: -0.21875 + 2.44140625 = 2.22265625 2.44140625 + 3.125t + t2 = 2.22265625 Factor a perfect square on the left side: (t + 1.5625)(t + 1.5625) = 2.22265625 Calculate the square root of the right side: 1.490857555 Break this problem into two subproblems by setting (t + 1.5625) equal to 1.490857555 and -1.490857555.Subproblem 1
t + 1.5625 = 1.490857555 Simplifying t + 1.5625 = 1.490857555 Reorder the terms: 1.5625 + t = 1.490857555 Solving 1.5625 + t = 1.490857555 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 = 1.490857555 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = 1.490857555 + -1.5625 t = 1.490857555 + -1.5625 Combine like terms: 1.490857555 + -1.5625 = -0.071642445 t = -0.071642445 Simplifying t = -0.071642445Subproblem 2
t + 1.5625 = -1.490857555 Simplifying t + 1.5625 = -1.490857555 Reorder the terms: 1.5625 + t = -1.490857555 Solving 1.5625 + t = -1.490857555 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 = -1.490857555 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + t = -1.490857555 + -1.5625 t = -1.490857555 + -1.5625 Combine like terms: -1.490857555 + -1.5625 = -3.053357555 t = -3.053357555 Simplifying t = -3.053357555Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.071642445, -3.053357555}
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