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Simplifying 9t2 + -1t + -9 = 0 Reorder the terms: -9 + -1t + 9t2 = 0 Solving -9 + -1t + 9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1 + -0.1111111111t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.1111111111t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -0.1111111111t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.1111111111t + t2 = 0 + 1 -0.1111111111t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.1111111111t + t2 = 1 The t term is -0.1111111111t. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111t + 0.003086419752 + t2 = 1 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111t + t2 = 1 + 0.003086419752 Combine like terms: 1 + 0.003086419752 = 1.003086419752 0.003086419752 + -0.1111111111t + t2 = 1.003086419752 Factor a perfect square on the left side: (t + -0.05555555555)(t + -0.05555555555) = 1.003086419752 Calculate the square root of the right side: 1.001542021 Break this problem into two subproblems by setting (t + -0.05555555555) equal to 1.001542021 and -1.001542021.Subproblem 1
t + -0.05555555555 = 1.001542021 Simplifying t + -0.05555555555 = 1.001542021 Reorder the terms: -0.05555555555 + t = 1.001542021 Solving -0.05555555555 + t = 1.001542021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + t = 1.001542021 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + t = 1.001542021 + 0.05555555555 t = 1.001542021 + 0.05555555555 Combine like terms: 1.001542021 + 0.05555555555 = 1.05709757655 t = 1.05709757655 Simplifying t = 1.05709757655Subproblem 2
t + -0.05555555555 = -1.001542021 Simplifying t + -0.05555555555 = -1.001542021 Reorder the terms: -0.05555555555 + t = -1.001542021 Solving -0.05555555555 + t = -1.001542021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + t = -1.001542021 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + t = -1.001542021 + 0.05555555555 t = -1.001542021 + 0.05555555555 Combine like terms: -1.001542021 + 0.05555555555 = -0.94598646545 t = -0.94598646545 Simplifying t = -0.94598646545Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.05709757655, -0.94598646545}
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