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Simplifying 2t2 + 81t + -1190 = 0 Reorder the terms: -1190 + 81t + 2t2 = 0 Solving -1190 + 81t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -595 + 40.5t + t2 = 0 Move the constant term to the right: Add '595' to each side of the equation. -595 + 40.5t + 595 + t2 = 0 + 595 Reorder the terms: -595 + 595 + 40.5t + t2 = 0 + 595 Combine like terms: -595 + 595 = 0 0 + 40.5t + t2 = 0 + 595 40.5t + t2 = 0 + 595 Combine like terms: 0 + 595 = 595 40.5t + t2 = 595 The t term is 40.5t. Take half its coefficient (20.25). Square it (410.0625) and add it to both sides. Add '410.0625' to each side of the equation. 40.5t + 410.0625 + t2 = 595 + 410.0625 Reorder the terms: 410.0625 + 40.5t + t2 = 595 + 410.0625 Combine like terms: 595 + 410.0625 = 1005.0625 410.0625 + 40.5t + t2 = 1005.0625 Factor a perfect square on the left side: (t + 20.25)(t + 20.25) = 1005.0625 Calculate the square root of the right side: 31.702720703 Break this problem into two subproblems by setting (t + 20.25) equal to 31.702720703 and -31.702720703.Subproblem 1
t + 20.25 = 31.702720703 Simplifying t + 20.25 = 31.702720703 Reorder the terms: 20.25 + t = 31.702720703 Solving 20.25 + t = 31.702720703 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20.25' to each side of the equation. 20.25 + -20.25 + t = 31.702720703 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + t = 31.702720703 + -20.25 t = 31.702720703 + -20.25 Combine like terms: 31.702720703 + -20.25 = 11.452720703 t = 11.452720703 Simplifying t = 11.452720703Subproblem 2
t + 20.25 = -31.702720703 Simplifying t + 20.25 = -31.702720703 Reorder the terms: 20.25 + t = -31.702720703 Solving 20.25 + t = -31.702720703 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-20.25' to each side of the equation. 20.25 + -20.25 + t = -31.702720703 + -20.25 Combine like terms: 20.25 + -20.25 = 0.00 0.00 + t = -31.702720703 + -20.25 t = -31.702720703 + -20.25 Combine like terms: -31.702720703 + -20.25 = -51.952720703 t = -51.952720703 Simplifying t = -51.952720703Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.452720703, -51.952720703}
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