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Simplifying 2t2 + -11t + 2 = 0 Reorder the terms: 2 + -11t + 2t2 = 0 Solving 2 + -11t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + -5.5t + t2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5.5t + -1 + t2 = 0 + -1 Reorder the terms: 1 + -1 + -5.5t + t2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5.5t + t2 = 0 + -1 -5.5t + t2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5.5t + t2 = -1 The t term is -5.5t. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5t + 7.5625 + t2 = -1 + 7.5625 Reorder the terms: 7.5625 + -5.5t + t2 = -1 + 7.5625 Combine like terms: -1 + 7.5625 = 6.5625 7.5625 + -5.5t + t2 = 6.5625 Factor a perfect square on the left side: (t + -2.75)(t + -2.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (t + -2.75) equal to 2.561737691 and -2.561737691.Subproblem 1
t + -2.75 = 2.561737691 Simplifying t + -2.75 = 2.561737691 Reorder the terms: -2.75 + t = 2.561737691 Solving -2.75 + t = 2.561737691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = 2.561737691 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = 2.561737691 + 2.75 t = 2.561737691 + 2.75 Combine like terms: 2.561737691 + 2.75 = 5.311737691 t = 5.311737691 Simplifying t = 5.311737691Subproblem 2
t + -2.75 = -2.561737691 Simplifying t + -2.75 = -2.561737691 Reorder the terms: -2.75 + t = -2.561737691 Solving -2.75 + t = -2.561737691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + t = -2.561737691 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + t = -2.561737691 + 2.75 t = -2.561737691 + 2.75 Combine like terms: -2.561737691 + 2.75 = 0.188262309 t = 0.188262309 Simplifying t = 0.188262309Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.311737691, 0.188262309}
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