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Simplifying 3t2 + -36t + 8 = 0 Reorder the terms: 8 + -36t + 3t2 = 0 Solving 8 + -36t + 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'. 2.666666667 + -12t + t2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -12t + -2.666666667 + t2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -12t + t2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -12t + t2 = 0 + -2.666666667 -12t + t2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -12t + t2 = -2.666666667 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = -2.666666667 + 36 Reorder the terms: 36 + -12t + t2 = -2.666666667 + 36 Combine like terms: -2.666666667 + 36 = 33.333333333 36 + -12t + t2 = 33.333333333 Factor a perfect square on the left side: (t + -6)(t + -6) = 33.333333333 Calculate the square root of the right side: 5.773502692 Break this problem into two subproblems by setting (t + -6) equal to 5.773502692 and -5.773502692.Subproblem 1
t + -6 = 5.773502692 Simplifying t + -6 = 5.773502692 Reorder the terms: -6 + t = 5.773502692 Solving -6 + t = 5.773502692 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 5.773502692 + 6 Combine like terms: -6 + 6 = 0 0 + t = 5.773502692 + 6 t = 5.773502692 + 6 Combine like terms: 5.773502692 + 6 = 11.773502692 t = 11.773502692 Simplifying t = 11.773502692Subproblem 2
t + -6 = -5.773502692 Simplifying t + -6 = -5.773502692 Reorder the terms: -6 + t = -5.773502692 Solving -6 + t = -5.773502692 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -5.773502692 + 6 Combine like terms: -6 + 6 = 0 0 + t = -5.773502692 + 6 t = -5.773502692 + 6 Combine like terms: -5.773502692 + 6 = 0.226497308 t = 0.226497308 Simplifying t = 0.226497308Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.773502692, 0.226497308}
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