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Simplifying 14t2 + 14t + -15 = 0 Reorder the terms: -15 + 14t + 14t2 = 0 Solving -15 + 14t + 14t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.071428571 + t + t2 = 0 Move the constant term to the right: Add '1.071428571' to each side of the equation. -1.071428571 + t + 1.071428571 + t2 = 0 + 1.071428571 Reorder the terms: -1.071428571 + 1.071428571 + t + t2 = 0 + 1.071428571 Combine like terms: -1.071428571 + 1.071428571 = 0.000000000 0.000000000 + t + t2 = 0 + 1.071428571 t + t2 = 0 + 1.071428571 Combine like terms: 0 + 1.071428571 = 1.071428571 t + t2 = 1.071428571 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 1.071428571 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 1.071428571 + 0.25 Combine like terms: 1.071428571 + 0.25 = 1.321428571 1.25 + t2 = 1.321428571 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 1.321428571 Calculate the square root of the right side: 1.149534067 Break this problem into two subproblems by setting (t + 0.5) equal to 1.149534067 and -1.149534067.Subproblem 1
t + 0.5 = 1.149534067 Simplifying t + 0.5 = 1.149534067 Reorder the terms: 0.5 + t = 1.149534067 Solving 0.5 + t = 1.149534067 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 1.149534067 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.149534067 + -0.5 t = 1.149534067 + -0.5 Combine like terms: 1.149534067 + -0.5 = 0.649534067 t = 0.649534067 Simplifying t = 0.649534067Subproblem 2
t + 0.5 = -1.149534067 Simplifying t + 0.5 = -1.149534067 Reorder the terms: 0.5 + t = -1.149534067 Solving 0.5 + t = -1.149534067 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -1.149534067 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.149534067 + -0.5 t = -1.149534067 + -0.5 Combine like terms: -1.149534067 + -0.5 = -1.649534067 t = -1.649534067 Simplifying t = -1.649534067Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.649534067, -1.649534067}
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