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Simplifying 0 = 5t2 + 2t + -43 Reorder the terms: 0 = -43 + 2t + 5t2 Solving 0 = -43 + 2t + 5t2 Solving for variable 't'. Combine like terms: 0 + 43 = 43 43 + -2t + -5t2 = -43 + 2t + 5t2 + 43 + -2t + -5t2 Reorder the terms: 43 + -2t + -5t2 = -43 + 43 + 2t + -2t + 5t2 + -5t2 Combine like terms: -43 + 43 = 0 43 + -2t + -5t2 = 0 + 2t + -2t + 5t2 + -5t2 43 + -2t + -5t2 = 2t + -2t + 5t2 + -5t2 Combine like terms: 2t + -2t = 0 43 + -2t + -5t2 = 0 + 5t2 + -5t2 43 + -2t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 43 + -2t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -8.6 + 0.4t + t2 = 0 Move the constant term to the right: Add '8.6' to each side of the equation. -8.6 + 0.4t + 8.6 + t2 = 0 + 8.6 Reorder the terms: -8.6 + 8.6 + 0.4t + t2 = 0 + 8.6 Combine like terms: -8.6 + 8.6 = 0.0 0.0 + 0.4t + t2 = 0 + 8.6 0.4t + t2 = 0 + 8.6 Combine like terms: 0 + 8.6 = 8.6 0.4t + t2 = 8.6 The t term is 0.4t. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4t + 0.04 + t2 = 8.6 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 8.6 + 0.04 Combine like terms: 8.6 + 0.04 = 8.64 0.04 + 0.4t + t2 = 8.64 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 8.64 Calculate the square root of the right side: 2.939387691 Break this problem into two subproblems by setting (t + 0.2) equal to 2.939387691 and -2.939387691.Subproblem 1
t + 0.2 = 2.939387691 Simplifying t + 0.2 = 2.939387691 Reorder the terms: 0.2 + t = 2.939387691 Solving 0.2 + t = 2.939387691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = 2.939387691 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 2.939387691 + -0.2 t = 2.939387691 + -0.2 Combine like terms: 2.939387691 + -0.2 = 2.739387691 t = 2.739387691 Simplifying t = 2.739387691Subproblem 2
t + 0.2 = -2.939387691 Simplifying t + 0.2 = -2.939387691 Reorder the terms: 0.2 + t = -2.939387691 Solving 0.2 + t = -2.939387691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + t = -2.939387691 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -2.939387691 + -0.2 t = -2.939387691 + -0.2 Combine like terms: -2.939387691 + -0.2 = -3.139387691 t = -3.139387691 Simplifying t = -3.139387691Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.739387691, -3.139387691}
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