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Simplifying 5t2 = 5 + -6t Solving 5t2 = 5 + -6t Solving for variable 't'. Reorder the terms: -5 + 6t + 5t2 = 5 + -6t + -5 + 6t Reorder the terms: -5 + 6t + 5t2 = 5 + -5 + -6t + 6t Combine like terms: 5 + -5 = 0 -5 + 6t + 5t2 = 0 + -6t + 6t -5 + 6t + 5t2 = -6t + 6t Combine like terms: -6t + 6t = 0 -5 + 6t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + 1.2t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.2t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + 1.2t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.2t + t2 = 0 + 1 1.2t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.2t + t2 = 1 The t term is 1.2t. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2t + 0.36 + t2 = 1 + 0.36 Reorder the terms: 0.36 + 1.2t + t2 = 1 + 0.36 Combine like terms: 1 + 0.36 = 1.36 0.36 + 1.2t + t2 = 1.36 Factor a perfect square on the left side: (t + 0.6)(t + 0.6) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (t + 0.6) equal to 1.166190379 and -1.166190379.Subproblem 1
t + 0.6 = 1.166190379 Simplifying t + 0.6 = 1.166190379 Reorder the terms: 0.6 + t = 1.166190379 Solving 0.6 + t = 1.166190379 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = 1.166190379 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = 1.166190379 + -0.6 t = 1.166190379 + -0.6 Combine like terms: 1.166190379 + -0.6 = 0.566190379 t = 0.566190379 Simplifying t = 0.566190379Subproblem 2
t + 0.6 = -1.166190379 Simplifying t + 0.6 = -1.166190379 Reorder the terms: 0.6 + t = -1.166190379 Solving 0.6 + t = -1.166190379 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + t = -1.166190379 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + t = -1.166190379 + -0.6 t = -1.166190379 + -0.6 Combine like terms: -1.166190379 + -0.6 = -1.766190379 t = -1.766190379 Simplifying t = -1.766190379Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.566190379, -1.766190379}
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