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Simplifying 3t2 + -6t + -28 = 0 Reorder the terms: -28 + -6t + 3t2 = 0 Solving -28 + -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'. -9.333333333 + -2t + t2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -2t + 9.333333333 + t2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -2t + t2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -2t + t2 = 0 + 9.333333333 -2t + t2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -2t + t2 = 9.333333333 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 = 9.333333333 + 1 Reorder the terms: 1 + -2t + t2 = 9.333333333 + 1 Combine like terms: 9.333333333 + 1 = 10.333333333 1 + -2t + t2 = 10.333333333 Factor a perfect square on the left side: (t + -1)(t + -1) = 10.333333333 Calculate the square root of the right side: 3.214550254 Break this problem into two subproblems by setting (t + -1) equal to 3.214550254 and -3.214550254.Subproblem 1
t + -1 = 3.214550254 Simplifying t + -1 = 3.214550254 Reorder the terms: -1 + t = 3.214550254 Solving -1 + t = 3.214550254 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 = 3.214550254 + 1 Combine like terms: -1 + 1 = 0 0 + t = 3.214550254 + 1 t = 3.214550254 + 1 Combine like terms: 3.214550254 + 1 = 4.214550254 t = 4.214550254 Simplifying t = 4.214550254Subproblem 2
t + -1 = -3.214550254 Simplifying t + -1 = -3.214550254 Reorder the terms: -1 + t = -3.214550254 Solving -1 + t = -3.214550254 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 = -3.214550254 + 1 Combine like terms: -1 + 1 = 0 0 + t = -3.214550254 + 1 t = -3.214550254 + 1 Combine like terms: -3.214550254 + 1 = -2.214550254 t = -2.214550254 Simplifying t = -2.214550254Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.214550254, -2.214550254}
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