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Simplifying -9t2 + -2t + 8 = 0 Reorder the terms: 8 + -2t + -9t2 = 0 Solving 8 + -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'. -0.8888888889 + 0.2222222222t + t2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.2222222222t + 0.8888888889 + t2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.2222222222t + t2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.2222222222t + t2 = 0 + 0.8888888889 0.2222222222t + t2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.2222222222t + t2 = 0.8888888889 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 = 0.8888888889 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222t + t2 = 0.8888888889 + 0.01234567901 Combine like terms: 0.8888888889 + 0.01234567901 = 0.90123456791 0.01234567901 + 0.2222222222t + t2 = 0.90123456791 Factor a perfect square on the left side: (t + 0.1111111111)(t + 0.1111111111) = 0.90123456791 Calculate the square root of the right side: 0.949333749 Break this problem into two subproblems by setting (t + 0.1111111111) equal to 0.949333749 and -0.949333749.Subproblem 1
t + 0.1111111111 = 0.949333749 Simplifying t + 0.1111111111 = 0.949333749 Reorder the terms: 0.1111111111 + t = 0.949333749 Solving 0.1111111111 + t = 0.949333749 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 = 0.949333749 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + t = 0.949333749 + -0.1111111111 t = 0.949333749 + -0.1111111111 Combine like terms: 0.949333749 + -0.1111111111 = 0.8382226379 t = 0.8382226379 Simplifying t = 0.8382226379Subproblem 2
t + 0.1111111111 = -0.949333749 Simplifying t + 0.1111111111 = -0.949333749 Reorder the terms: 0.1111111111 + t = -0.949333749 Solving 0.1111111111 + t = -0.949333749 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 = -0.949333749 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + t = -0.949333749 + -0.1111111111 t = -0.949333749 + -0.1111111111 Combine like terms: -0.949333749 + -0.1111111111 = -1.0604448601 t = -1.0604448601 Simplifying t = -1.0604448601Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.8382226379, -1.0604448601}
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