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Simplifying 5t2 + 14t + 3 = 0 Reorder the terms: 3 + 14t + 5t2 = 0 Solving 3 + 14t + 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'. 0.6 + 2.8t + t2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 2.8t + -0.6 + t2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 2.8t + t2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 2.8t + t2 = 0 + -0.6 2.8t + t2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 2.8t + t2 = -0.6 The t term is 2.8t. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8t + 1.96 + t2 = -0.6 + 1.96 Reorder the terms: 1.96 + 2.8t + t2 = -0.6 + 1.96 Combine like terms: -0.6 + 1.96 = 1.36 1.96 + 2.8t + t2 = 1.36 Factor a perfect square on the left side: (t + 1.4)(t + 1.4) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (t + 1.4) equal to 1.166190379 and -1.166190379.Subproblem 1
t + 1.4 = 1.166190379 Simplifying t + 1.4 = 1.166190379 Reorder the terms: 1.4 + t = 1.166190379 Solving 1.4 + t = 1.166190379 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + t = 1.166190379 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + t = 1.166190379 + -1.4 t = 1.166190379 + -1.4 Combine like terms: 1.166190379 + -1.4 = -0.233809621 t = -0.233809621 Simplifying t = -0.233809621Subproblem 2
t + 1.4 = -1.166190379 Simplifying t + 1.4 = -1.166190379 Reorder the terms: 1.4 + t = -1.166190379 Solving 1.4 + t = -1.166190379 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + t = -1.166190379 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + t = -1.166190379 + -1.4 t = -1.166190379 + -1.4 Combine like terms: -1.166190379 + -1.4 = -2.566190379 t = -2.566190379 Simplifying t = -2.566190379Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.233809621, -2.566190379}
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