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Simplifying 1.6t2 = 2.5t2 + -20t + 40 Reorder the terms: 1.6t2 = 40 + -20t + 2.5t2 Solving 1.6t2 = 40 + -20t + 2.5t2 Solving for variable 't'. Reorder the terms: -40 + 20t + 1.6t2 + -2.5t2 = 40 + -20t + 2.5t2 + -40 + 20t + -2.5t2 Combine like terms: 1.6t2 + -2.5t2 = -0.9t2 -40 + 20t + -0.9t2 = 40 + -20t + 2.5t2 + -40 + 20t + -2.5t2 Reorder the terms: -40 + 20t + -0.9t2 = 40 + -40 + -20t + 20t + 2.5t2 + -2.5t2 Combine like terms: 40 + -40 = 0 -40 + 20t + -0.9t2 = 0 + -20t + 20t + 2.5t2 + -2.5t2 -40 + 20t + -0.9t2 = -20t + 20t + 2.5t2 + -2.5t2 Combine like terms: -20t + 20t = 0 -40 + 20t + -0.9t2 = 0 + 2.5t2 + -2.5t2 -40 + 20t + -0.9t2 = 2.5t2 + -2.5t2 Combine like terms: 2.5t2 + -2.5t2 = 0.0 -40 + 20t + -0.9t2 = 0.0 Begin completing the square. Divide all terms by -0.9 the coefficient of the squared term: Divide each side by '-0.9'. 44.44444444 + -22.22222222t + t2 = 0 Move the constant term to the right: Add '-44.44444444' to each side of the equation. 44.44444444 + -22.22222222t + -44.44444444 + t2 = 0 + -44.44444444 Reorder the terms: 44.44444444 + -44.44444444 + -22.22222222t + t2 = 0 + -44.44444444 Combine like terms: 44.44444444 + -44.44444444 = 0.00000000 0.00000000 + -22.22222222t + t2 = 0 + -44.44444444 -22.22222222t + t2 = 0 + -44.44444444 Combine like terms: 0 + -44.44444444 = -44.44444444 -22.22222222t + t2 = -44.44444444 The t term is -22.22222222t. Take half its coefficient (-11.11111111). Square it (123.4567901) and add it to both sides. Add '123.4567901' to each side of the equation. -22.22222222t + 123.4567901 + t2 = -44.44444444 + 123.4567901 Reorder the terms: 123.4567901 + -22.22222222t + t2 = -44.44444444 + 123.4567901 Combine like terms: -44.44444444 + 123.4567901 = 79.01234566 123.4567901 + -22.22222222t + t2 = 79.01234566 Factor a perfect square on the left side: (t + -11.11111111)(t + -11.11111111) = 79.01234566 Calculate the square root of the right side: 8.888888888 Break this problem into two subproblems by setting (t + -11.11111111) equal to 8.888888888 and -8.888888888.Subproblem 1
t + -11.11111111 = 8.888888888 Simplifying t + -11.11111111 = 8.888888888 Reorder the terms: -11.11111111 + t = 8.888888888 Solving -11.11111111 + t = 8.888888888 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.11111111' to each side of the equation. -11.11111111 + 11.11111111 + t = 8.888888888 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + t = 8.888888888 + 11.11111111 t = 8.888888888 + 11.11111111 Combine like terms: 8.888888888 + 11.11111111 = 19.999999998 t = 19.999999998 Simplifying t = 19.999999998Subproblem 2
t + -11.11111111 = -8.888888888 Simplifying t + -11.11111111 = -8.888888888 Reorder the terms: -11.11111111 + t = -8.888888888 Solving -11.11111111 + t = -8.888888888 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.11111111' to each side of the equation. -11.11111111 + 11.11111111 + t = -8.888888888 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + t = -8.888888888 + 11.11111111 t = -8.888888888 + 11.11111111 Combine like terms: -8.888888888 + 11.11111111 = 2.222222222 t = 2.222222222 Simplifying t = 2.222222222Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.999999998, 2.222222222}
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