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Simplifying 3t2 + 6t + -11 = 0 Reorder the terms: -11 + 6t + 3t2 = 0 Solving -11 + 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'. -3.666666667 + 2t + t2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 2t + 3.666666667 + t2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 2t + t2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 2t + t2 = 0 + 3.666666667 2t + t2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 2t + t2 = 3.666666667 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 = 3.666666667 + 1 Reorder the terms: 1 + 2t + t2 = 3.666666667 + 1 Combine like terms: 3.666666667 + 1 = 4.666666667 1 + 2t + t2 = 4.666666667 Factor a perfect square on the left side: (t + 1)(t + 1) = 4.666666667 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (t + 1) equal to 2.1602469 and -2.1602469.Subproblem 1
t + 1 = 2.1602469 Simplifying t + 1 = 2.1602469 Reorder the terms: 1 + t = 2.1602469 Solving 1 + t = 2.1602469 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 = 2.1602469 + -1 Combine like terms: 1 + -1 = 0 0 + t = 2.1602469 + -1 t = 2.1602469 + -1 Combine like terms: 2.1602469 + -1 = 1.1602469 t = 1.1602469 Simplifying t = 1.1602469Subproblem 2
t + 1 = -2.1602469 Simplifying t + 1 = -2.1602469 Reorder the terms: 1 + t = -2.1602469 Solving 1 + t = -2.1602469 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 = -2.1602469 + -1 Combine like terms: 1 + -1 = 0 0 + t = -2.1602469 + -1 t = -2.1602469 + -1 Combine like terms: -2.1602469 + -1 = -3.1602469 t = -3.1602469 Simplifying t = -3.1602469Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.1602469, -3.1602469}
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