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Simplifying 5t2 = 5 + -2t Solving 5t2 = 5 + -2t Solving for variable 't'. Reorder the terms: -5 + 2t + 5t2 = 5 + -2t + -5 + 2t Reorder the terms: -5 + 2t + 5t2 = 5 + -5 + -2t + 2t Combine like terms: 5 + -5 = 0 -5 + 2t + 5t2 = 0 + -2t + 2t -5 + 2t + 5t2 = -2t + 2t Combine like terms: -2t + 2t = 0 -5 + 2t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + 0.4t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.4t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + 0.4t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.4t + t2 = 0 + 1 0.4t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.4t + t2 = 1 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 = 1 + 0.04 Reorder the terms: 0.04 + 0.4t + t2 = 1 + 0.04 Combine like terms: 1 + 0.04 = 1.04 0.04 + 0.4t + t2 = 1.04 Factor a perfect square on the left side: (t + 0.2)(t + 0.2) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (t + 0.2) equal to 1.019803903 and -1.019803903.Subproblem 1
t + 0.2 = 1.019803903 Simplifying t + 0.2 = 1.019803903 Reorder the terms: 0.2 + t = 1.019803903 Solving 0.2 + t = 1.019803903 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 = 1.019803903 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = 1.019803903 + -0.2 t = 1.019803903 + -0.2 Combine like terms: 1.019803903 + -0.2 = 0.819803903 t = 0.819803903 Simplifying t = 0.819803903Subproblem 2
t + 0.2 = -1.019803903 Simplifying t + 0.2 = -1.019803903 Reorder the terms: 0.2 + t = -1.019803903 Solving 0.2 + t = -1.019803903 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 = -1.019803903 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + t = -1.019803903 + -0.2 t = -1.019803903 + -0.2 Combine like terms: -1.019803903 + -0.2 = -1.219803903 t = -1.219803903 Simplifying t = -1.219803903Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.819803903, -1.219803903}
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