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Simplifying 3t2 + -8t + -36 = 0 Reorder the terms: -36 + -8t + 3t2 = 0 Solving -36 + -8t + 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'. -12 + -2.666666667t + t2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -2.666666667t + 12 + t2 = 0 + 12 Reorder the terms: -12 + 12 + -2.666666667t + t2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2.666666667t + t2 = 0 + 12 -2.666666667t + t2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2.666666667t + t2 = 12 The t term is -2.666666667t. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667t + 1.777777780 + t2 = 12 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667t + t2 = 12 + 1.777777780 Combine like terms: 12 + 1.777777780 = 13.77777778 1.777777780 + -2.666666667t + t2 = 13.77777778 Factor a perfect square on the left side: (t + -1.333333334)(t + -1.333333334) = 13.77777778 Calculate the square root of the right side: 3.711842909 Break this problem into two subproblems by setting (t + -1.333333334) equal to 3.711842909 and -3.711842909.Subproblem 1
t + -1.333333334 = 3.711842909 Simplifying t + -1.333333334 = 3.711842909 Reorder the terms: -1.333333334 + t = 3.711842909 Solving -1.333333334 + t = 3.711842909 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + t = 3.711842909 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = 3.711842909 + 1.333333334 t = 3.711842909 + 1.333333334 Combine like terms: 3.711842909 + 1.333333334 = 5.045176243 t = 5.045176243 Simplifying t = 5.045176243Subproblem 2
t + -1.333333334 = -3.711842909 Simplifying t + -1.333333334 = -3.711842909 Reorder the terms: -1.333333334 + t = -3.711842909 Solving -1.333333334 + t = -3.711842909 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + t = -3.711842909 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = -3.711842909 + 1.333333334 t = -3.711842909 + 1.333333334 Combine like terms: -3.711842909 + 1.333333334 = -2.378509575 t = -2.378509575 Simplifying t = -2.378509575Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.045176243, -2.378509575}
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