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Simplifying 2t2 + 19t + -9 = 0 Reorder the terms: -9 + 19t + 2t2 = 0 Solving -9 + 19t + 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'. -4.5 + 9.5t + t2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 9.5t + 4.5 + t2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 9.5t + t2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 9.5t + t2 = 0 + 4.5 9.5t + t2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 9.5t + t2 = 4.5 The t term is 9.5t. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5t + 22.5625 + t2 = 4.5 + 22.5625 Reorder the terms: 22.5625 + 9.5t + t2 = 4.5 + 22.5625 Combine like terms: 4.5 + 22.5625 = 27.0625 22.5625 + 9.5t + t2 = 27.0625 Factor a perfect square on the left side: (t + 4.75)(t + 4.75) = 27.0625 Calculate the square root of the right side: 5.202163012 Break this problem into two subproblems by setting (t + 4.75) equal to 5.202163012 and -5.202163012.Subproblem 1
t + 4.75 = 5.202163012 Simplifying t + 4.75 = 5.202163012 Reorder the terms: 4.75 + t = 5.202163012 Solving 4.75 + t = 5.202163012 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + t = 5.202163012 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + t = 5.202163012 + -4.75 t = 5.202163012 + -4.75 Combine like terms: 5.202163012 + -4.75 = 0.452163012 t = 0.452163012 Simplifying t = 0.452163012Subproblem 2
t + 4.75 = -5.202163012 Simplifying t + 4.75 = -5.202163012 Reorder the terms: 4.75 + t = -5.202163012 Solving 4.75 + t = -5.202163012 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + t = -5.202163012 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + t = -5.202163012 + -4.75 t = -5.202163012 + -4.75 Combine like terms: -5.202163012 + -4.75 = -9.952163012 t = -9.952163012 Simplifying t = -9.952163012Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.452163012, -9.952163012}
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