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Simplifying 3t2 + -18t + 4 = 0 Reorder the terms: 4 + -18t + 3t2 = 0 Solving 4 + -18t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -6t + t2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -6t + -1.333333333 + t2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -6t + t2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -6t + t2 = 0 + -1.333333333 -6t + t2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -6t + t2 = -1.333333333 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -1.333333333 + 9 Reorder the terms: 9 + -6t + t2 = -1.333333333 + 9 Combine like terms: -1.333333333 + 9 = 7.666666667 9 + -6t + t2 = 7.666666667 Factor a perfect square on the left side: (t + -3)(t + -3) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (t + -3) equal to 2.768874621 and -2.768874621.Subproblem 1
t + -3 = 2.768874621 Simplifying t + -3 = 2.768874621 Reorder the terms: -3 + t = 2.768874621 Solving -3 + t = 2.768874621 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.768874621 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.768874621 + 3 t = 2.768874621 + 3 Combine like terms: 2.768874621 + 3 = 5.768874621 t = 5.768874621 Simplifying t = 5.768874621Subproblem 2
t + -3 = -2.768874621 Simplifying t + -3 = -2.768874621 Reorder the terms: -3 + t = -2.768874621 Solving -3 + t = -2.768874621 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.768874621 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.768874621 + 3 t = -2.768874621 + 3 Combine like terms: -2.768874621 + 3 = 0.231125379 t = 0.231125379 Simplifying t = 0.231125379Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.768874621, 0.231125379}
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