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Simplifying 11t2 + -9t + -819 = 0 Reorder the terms: -819 + -9t + 11t2 = 0 Solving -819 + -9t + 11t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -74.45454545 + -0.8181818182t + t2 = 0 Move the constant term to the right: Add '74.45454545' to each side of the equation. -74.45454545 + -0.8181818182t + 74.45454545 + t2 = 0 + 74.45454545 Reorder the terms: -74.45454545 + 74.45454545 + -0.8181818182t + t2 = 0 + 74.45454545 Combine like terms: -74.45454545 + 74.45454545 = 0.00000000 0.00000000 + -0.8181818182t + t2 = 0 + 74.45454545 -0.8181818182t + t2 = 0 + 74.45454545 Combine like terms: 0 + 74.45454545 = 74.45454545 -0.8181818182t + t2 = 74.45454545 The t term is -0.8181818182t. Take half its coefficient (-0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. -0.8181818182t + 0.1673553719 + t2 = 74.45454545 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182t + t2 = 74.45454545 + 0.1673553719 Combine like terms: 74.45454545 + 0.1673553719 = 74.6219008219 0.1673553719 + -0.8181818182t + t2 = 74.6219008219 Factor a perfect square on the left side: (t + -0.4090909091)(t + -0.4090909091) = 74.6219008219 Calculate the square root of the right side: 8.63839689 Break this problem into two subproblems by setting (t + -0.4090909091) equal to 8.63839689 and -8.63839689.Subproblem 1
t + -0.4090909091 = 8.63839689 Simplifying t + -0.4090909091 = 8.63839689 Reorder the terms: -0.4090909091 + t = 8.63839689 Solving -0.4090909091 + t = 8.63839689 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + t = 8.63839689 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + t = 8.63839689 + 0.4090909091 t = 8.63839689 + 0.4090909091 Combine like terms: 8.63839689 + 0.4090909091 = 9.0474877991 t = 9.0474877991 Simplifying t = 9.0474877991Subproblem 2
t + -0.4090909091 = -8.63839689 Simplifying t + -0.4090909091 = -8.63839689 Reorder the terms: -0.4090909091 + t = -8.63839689 Solving -0.4090909091 + t = -8.63839689 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + t = -8.63839689 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + t = -8.63839689 + 0.4090909091 t = -8.63839689 + 0.4090909091 Combine like terms: -8.63839689 + 0.4090909091 = -8.2293059809 t = -8.2293059809 Simplifying t = -8.2293059809Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.0474877991, -8.2293059809}
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