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Simplifying 0 = -26t2 + 44t + 5 Reorder the terms: 0 = 5 + 44t + -26t2 Solving 0 = 5 + 44t + -26t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -44t + 26t2 = 5 + 44t + -26t2 + -5 + -44t + 26t2 Reorder the terms: -5 + -44t + 26t2 = 5 + -5 + 44t + -44t + -26t2 + 26t2 Combine like terms: 5 + -5 = 0 -5 + -44t + 26t2 = 0 + 44t + -44t + -26t2 + 26t2 -5 + -44t + 26t2 = 44t + -44t + -26t2 + 26t2 Combine like terms: 44t + -44t = 0 -5 + -44t + 26t2 = 0 + -26t2 + 26t2 -5 + -44t + 26t2 = -26t2 + 26t2 Combine like terms: -26t2 + 26t2 = 0 -5 + -44t + 26t2 = 0 Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.1923076923 + -1.692307692t + t2 = 0 Move the constant term to the right: Add '0.1923076923' to each side of the equation. -0.1923076923 + -1.692307692t + 0.1923076923 + t2 = 0 + 0.1923076923 Reorder the terms: -0.1923076923 + 0.1923076923 + -1.692307692t + t2 = 0 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + -1.692307692t + t2 = 0 + 0.1923076923 -1.692307692t + t2 = 0 + 0.1923076923 Combine like terms: 0 + 0.1923076923 = 0.1923076923 -1.692307692t + t2 = 0.1923076923 The t term is -1.692307692t. Take half its coefficient (-0.846153846). Square it (0.7159763311) and add it to both sides. Add '0.7159763311' to each side of the equation. -1.692307692t + 0.7159763311 + t2 = 0.1923076923 + 0.7159763311 Reorder the terms: 0.7159763311 + -1.692307692t + t2 = 0.1923076923 + 0.7159763311 Combine like terms: 0.1923076923 + 0.7159763311 = 0.9082840234 0.7159763311 + -1.692307692t + t2 = 0.9082840234 Factor a perfect square on the left side: (t + -0.846153846)(t + -0.846153846) = 0.9082840234 Calculate the square root of the right side: 0.953039361 Break this problem into two subproblems by setting (t + -0.846153846) equal to 0.953039361 and -0.953039361.Subproblem 1
t + -0.846153846 = 0.953039361 Simplifying t + -0.846153846 = 0.953039361 Reorder the terms: -0.846153846 + t = 0.953039361 Solving -0.846153846 + t = 0.953039361 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.846153846' to each side of the equation. -0.846153846 + 0.846153846 + t = 0.953039361 + 0.846153846 Combine like terms: -0.846153846 + 0.846153846 = 0.000000000 0.000000000 + t = 0.953039361 + 0.846153846 t = 0.953039361 + 0.846153846 Combine like terms: 0.953039361 + 0.846153846 = 1.799193207 t = 1.799193207 Simplifying t = 1.799193207Subproblem 2
t + -0.846153846 = -0.953039361 Simplifying t + -0.846153846 = -0.953039361 Reorder the terms: -0.846153846 + t = -0.953039361 Solving -0.846153846 + t = -0.953039361 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.846153846' to each side of the equation. -0.846153846 + 0.846153846 + t = -0.953039361 + 0.846153846 Combine like terms: -0.846153846 + 0.846153846 = 0.000000000 0.000000000 + t = -0.953039361 + 0.846153846 t = -0.953039361 + 0.846153846 Combine like terms: -0.953039361 + 0.846153846 = -0.106885515 t = -0.106885515 Simplifying t = -0.106885515Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.799193207, -0.106885515}
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