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Simplifying 11t2 + 6t = 8 Reorder the terms: 6t + 11t2 = 8 Solving 6t + 11t2 = 8 Solving for variable 't'. Reorder the terms: -8 + 6t + 11t2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 6t + 11t2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + 0.5454545455t + t2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 0.5454545455t + 0.7272727273 + t2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 0.5454545455t + t2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 0.5454545455t + t2 = 0 + 0.7272727273 0.5454545455t + t2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 0.5454545455t + t2 = 0.7272727273 The t term is 0.5454545455t. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455t + 0.07438016533 + t2 = 0.7272727273 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455t + t2 = 0.7272727273 + 0.07438016533 Combine like terms: 0.7272727273 + 0.07438016533 = 0.80165289263 0.07438016533 + 0.5454545455t + t2 = 0.80165289263 Factor a perfect square on the left side: (t + 0.2727272728)(t + 0.2727272728) = 0.80165289263 Calculate the square root of the right side: 0.895350709 Break this problem into two subproblems by setting (t + 0.2727272728) equal to 0.895350709 and -0.895350709.Subproblem 1
t + 0.2727272728 = 0.895350709 Simplifying t + 0.2727272728 = 0.895350709 Reorder the terms: 0.2727272728 + t = 0.895350709 Solving 0.2727272728 + t = 0.895350709 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + t = 0.895350709 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + t = 0.895350709 + -0.2727272728 t = 0.895350709 + -0.2727272728 Combine like terms: 0.895350709 + -0.2727272728 = 0.6226234362 t = 0.6226234362 Simplifying t = 0.6226234362Subproblem 2
t + 0.2727272728 = -0.895350709 Simplifying t + 0.2727272728 = -0.895350709 Reorder the terms: 0.2727272728 + t = -0.895350709 Solving 0.2727272728 + t = -0.895350709 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + t = -0.895350709 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + t = -0.895350709 + -0.2727272728 t = -0.895350709 + -0.2727272728 Combine like terms: -0.895350709 + -0.2727272728 = -1.1680779818 t = -1.1680779818 Simplifying t = -1.1680779818Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6226234362, -1.1680779818}
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