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Simplifying 5t2 + 10t + -2 = 0 Reorder the terms: -2 + 10t + 5t2 = 0 Solving -2 + 10t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 2t + t2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2t + 0.4 + t2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2t + t2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2t + t2 = 0 + 0.4 2t + t2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2t + t2 = 0.4 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 0.4 + 1 Reorder the terms: 1 + 2t + t2 = 0.4 + 1 Combine like terms: 0.4 + 1 = 1.4 1 + 2t + t2 = 1.4 Factor a perfect square on the left side: (t + 1)(t + 1) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (t + 1) equal to 1.183215957 and -1.183215957.Subproblem 1
t + 1 = 1.183215957 Simplifying t + 1 = 1.183215957 Reorder the terms: 1 + t = 1.183215957 Solving 1 + t = 1.183215957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 1.183215957 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.183215957 + -1 t = 1.183215957 + -1 Combine like terms: 1.183215957 + -1 = 0.183215957 t = 0.183215957 Simplifying t = 0.183215957Subproblem 2
t + 1 = -1.183215957 Simplifying t + 1 = -1.183215957 Reorder the terms: 1 + t = -1.183215957 Solving 1 + t = -1.183215957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -1.183215957 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.183215957 + -1 t = -1.183215957 + -1 Combine like terms: -1.183215957 + -1 = -2.183215957 t = -2.183215957 Simplifying t = -2.183215957Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.183215957, -2.183215957}
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