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Simplifying 3t2 + -8t + -15 = 0 Reorder the terms: -15 + -8t + 3t2 = 0 Solving -15 + -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'. -5 + -2.666666667t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -2.666666667t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -2.666666667t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2.666666667t + t2 = 0 + 5 -2.666666667t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2.666666667t + t2 = 5 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 = 5 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667t + t2 = 5 + 1.777777780 Combine like terms: 5 + 1.777777780 = 6.77777778 1.777777780 + -2.666666667t + t2 = 6.77777778 Factor a perfect square on the left side: (t + -1.333333334)(t + -1.333333334) = 6.77777778 Calculate the square root of the right side: 2.603416559 Break this problem into two subproblems by setting (t + -1.333333334) equal to 2.603416559 and -2.603416559.Subproblem 1
t + -1.333333334 = 2.603416559 Simplifying t + -1.333333334 = 2.603416559 Reorder the terms: -1.333333334 + t = 2.603416559 Solving -1.333333334 + t = 2.603416559 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 = 2.603416559 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = 2.603416559 + 1.333333334 t = 2.603416559 + 1.333333334 Combine like terms: 2.603416559 + 1.333333334 = 3.936749893 t = 3.936749893 Simplifying t = 3.936749893Subproblem 2
t + -1.333333334 = -2.603416559 Simplifying t + -1.333333334 = -2.603416559 Reorder the terms: -1.333333334 + t = -2.603416559 Solving -1.333333334 + t = -2.603416559 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 = -2.603416559 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = -2.603416559 + 1.333333334 t = -2.603416559 + 1.333333334 Combine like terms: -2.603416559 + 1.333333334 = -1.270083225 t = -1.270083225 Simplifying t = -1.270083225Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.936749893, -1.270083225}
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