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Simplifying 2t2 + -19t + 36 = 0 Reorder the terms: 36 + -19t + 2t2 = 0 Solving 36 + -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'. 18 + -9.5t + t2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -9.5t + -18 + t2 = 0 + -18 Reorder the terms: 18 + -18 + -9.5t + t2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -9.5t + t2 = 0 + -18 -9.5t + t2 = 0 + -18 Combine like terms: 0 + -18 = -18 -9.5t + t2 = -18 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 = -18 + 22.5625 Reorder the terms: 22.5625 + -9.5t + t2 = -18 + 22.5625 Combine like terms: -18 + 22.5625 = 4.5625 22.5625 + -9.5t + t2 = 4.5625 Factor a perfect square on the left side: (t + -4.75)(t + -4.75) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (t + -4.75) equal to 2.136000936 and -2.136000936.Subproblem 1
t + -4.75 = 2.136000936 Simplifying t + -4.75 = 2.136000936 Reorder the terms: -4.75 + t = 2.136000936 Solving -4.75 + t = 2.136000936 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 = 2.136000936 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + t = 2.136000936 + 4.75 t = 2.136000936 + 4.75 Combine like terms: 2.136000936 + 4.75 = 6.886000936 t = 6.886000936 Simplifying t = 6.886000936Subproblem 2
t + -4.75 = -2.136000936 Simplifying t + -4.75 = -2.136000936 Reorder the terms: -4.75 + t = -2.136000936 Solving -4.75 + t = -2.136000936 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 = -2.136000936 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + t = -2.136000936 + 4.75 t = -2.136000936 + 4.75 Combine like terms: -2.136000936 + 4.75 = 2.613999064 t = 2.613999064 Simplifying t = 2.613999064Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.886000936, 2.613999064}
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