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Simplifying 3t2 + -6t + -22 = 0 Reorder the terms: -22 + -6t + 3t2 = 0 Solving -22 + -6t + 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'. -7.333333333 + -2t + t2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + -2t + 7.333333333 + t2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + -2t + t2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + -2t + t2 = 0 + 7.333333333 -2t + t2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 -2t + t2 = 7.333333333 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 7.333333333 + 1 Reorder the terms: 1 + -2t + t2 = 7.333333333 + 1 Combine like terms: 7.333333333 + 1 = 8.333333333 1 + -2t + t2 = 8.333333333 Factor a perfect square on the left side: (t + -1)(t + -1) = 8.333333333 Calculate the square root of the right side: 2.886751346 Break this problem into two subproblems by setting (t + -1) equal to 2.886751346 and -2.886751346.Subproblem 1
t + -1 = 2.886751346 Simplifying t + -1 = 2.886751346 Reorder the terms: -1 + t = 2.886751346 Solving -1 + t = 2.886751346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 2.886751346 + 1 Combine like terms: -1 + 1 = 0 0 + t = 2.886751346 + 1 t = 2.886751346 + 1 Combine like terms: 2.886751346 + 1 = 3.886751346 t = 3.886751346 Simplifying t = 3.886751346Subproblem 2
t + -1 = -2.886751346 Simplifying t + -1 = -2.886751346 Reorder the terms: -1 + t = -2.886751346 Solving -1 + t = -2.886751346 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -2.886751346 + 1 Combine like terms: -1 + 1 = 0 0 + t = -2.886751346 + 1 t = -2.886751346 + 1 Combine like terms: -2.886751346 + 1 = -1.886751346 t = -1.886751346 Simplifying t = -1.886751346Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.886751346, -1.886751346}
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