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Simplifying 9t2 + 2t + -2 = 0 Reorder the terms: -2 + 2t + 9t2 = 0 Solving -2 + 2t + 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'. -0.2222222222 + 0.2222222222t + t2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222t + 0.2222222222 + t2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 0.2222222222t + t2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 0.2222222222t + t2 = 0 + 0.2222222222 0.2222222222t + t2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 0.2222222222t + t2 = 0.2222222222 The t term is 0.2222222222t. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222t + 0.01234567901 + t2 = 0.2222222222 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222t + t2 = 0.2222222222 + 0.01234567901 Combine like terms: 0.2222222222 + 0.01234567901 = 0.23456790121 0.01234567901 + 0.2222222222t + t2 = 0.23456790121 Factor a perfect square on the left side: (t + 0.1111111111)(t + 0.1111111111) = 0.23456790121 Calculate the square root of the right side: 0.484322105 Break this problem into two subproblems by setting (t + 0.1111111111) equal to 0.484322105 and -0.484322105.Subproblem 1
t + 0.1111111111 = 0.484322105 Simplifying t + 0.1111111111 = 0.484322105 Reorder the terms: 0.1111111111 + t = 0.484322105 Solving 0.1111111111 + t = 0.484322105 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + t = 0.484322105 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + t = 0.484322105 + -0.1111111111 t = 0.484322105 + -0.1111111111 Combine like terms: 0.484322105 + -0.1111111111 = 0.3732109939 t = 0.3732109939 Simplifying t = 0.3732109939Subproblem 2
t + 0.1111111111 = -0.484322105 Simplifying t + 0.1111111111 = -0.484322105 Reorder the terms: 0.1111111111 + t = -0.484322105 Solving 0.1111111111 + t = -0.484322105 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + t = -0.484322105 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + t = -0.484322105 + -0.1111111111 t = -0.484322105 + -0.1111111111 Combine like terms: -0.484322105 + -0.1111111111 = -0.5954332161 t = -0.5954332161 Simplifying t = -0.5954332161Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.3732109939, -0.5954332161}
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