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Simplifying 0 = -2.7t2 + 27t + 6 Reorder the terms: 0 = 6 + 27t + -2.7t2 Solving 0 = 6 + 27t + -2.7t2 Solving for variable 't'. Combine like terms: 0 + -6 = -6 -6 + -27t + 2.7t2 = 6 + 27t + -2.7t2 + -6 + -27t + 2.7t2 Reorder the terms: -6 + -27t + 2.7t2 = 6 + -6 + 27t + -27t + -2.7t2 + 2.7t2 Combine like terms: 6 + -6 = 0 -6 + -27t + 2.7t2 = 0 + 27t + -27t + -2.7t2 + 2.7t2 -6 + -27t + 2.7t2 = 27t + -27t + -2.7t2 + 2.7t2 Combine like terms: 27t + -27t = 0 -6 + -27t + 2.7t2 = 0 + -2.7t2 + 2.7t2 -6 + -27t + 2.7t2 = -2.7t2 + 2.7t2 Combine like terms: -2.7t2 + 2.7t2 = 0.0 -6 + -27t + 2.7t2 = 0.0 Begin completing the square. Divide all terms by 2.7 the coefficient of the squared term: Divide each side by '2.7'. -2.222222222 + -10t + t2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -10t + 2.222222222 + t2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -10t + t2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -10t + t2 = 0 + 2.222222222 -10t + t2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -10t + t2 = 2.222222222 The t term is -10t. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10t + 25 + t2 = 2.222222222 + 25 Reorder the terms: 25 + -10t + t2 = 2.222222222 + 25 Combine like terms: 2.222222222 + 25 = 27.222222222 25 + -10t + t2 = 27.222222222 Factor a perfect square on the left side: (t + -5)(t + -5) = 27.222222222 Calculate the square root of the right side: 5.217491947 Break this problem into two subproblems by setting (t + -5) equal to 5.217491947 and -5.217491947.Subproblem 1
t + -5 = 5.217491947 Simplifying t + -5 = 5.217491947 Reorder the terms: -5 + t = 5.217491947 Solving -5 + t = 5.217491947 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.217491947 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.217491947 + 5 t = 5.217491947 + 5 Combine like terms: 5.217491947 + 5 = 10.217491947 t = 10.217491947 Simplifying t = 10.217491947Subproblem 2
t + -5 = -5.217491947 Simplifying t + -5 = -5.217491947 Reorder the terms: -5 + t = -5.217491947 Solving -5 + t = -5.217491947 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.217491947 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.217491947 + 5 t = -5.217491947 + 5 Combine like terms: -5.217491947 + 5 = -0.217491947 t = -0.217491947 Simplifying t = -0.217491947Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.217491947, -0.217491947}
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