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Simplifying 9t2 + -24t + -10 = 0 Reorder the terms: -10 + -24t + 9t2 = 0 Solving -10 + -24t + 9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -2.666666667t + t2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -2.666666667t + 1.111111111 + t2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -2.666666667t + t2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -2.666666667t + t2 = 0 + 1.111111111 -2.666666667t + t2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -2.666666667t + t2 = 1.111111111 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 = 1.111111111 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667t + t2 = 1.111111111 + 1.777777780 Combine like terms: 1.111111111 + 1.777777780 = 2.888888891 1.777777780 + -2.666666667t + t2 = 2.888888891 Factor a perfect square on the left side: (t + -1.333333334)(t + -1.333333334) = 2.888888891 Calculate the square root of the right side: 1.699673172 Break this problem into two subproblems by setting (t + -1.333333334) equal to 1.699673172 and -1.699673172.Subproblem 1
t + -1.333333334 = 1.699673172 Simplifying t + -1.333333334 = 1.699673172 Reorder the terms: -1.333333334 + t = 1.699673172 Solving -1.333333334 + t = 1.699673172 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 = 1.699673172 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = 1.699673172 + 1.333333334 t = 1.699673172 + 1.333333334 Combine like terms: 1.699673172 + 1.333333334 = 3.033006506 t = 3.033006506 Simplifying t = 3.033006506Subproblem 2
t + -1.333333334 = -1.699673172 Simplifying t + -1.333333334 = -1.699673172 Reorder the terms: -1.333333334 + t = -1.699673172 Solving -1.333333334 + t = -1.699673172 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 = -1.699673172 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = -1.699673172 + 1.333333334 t = -1.699673172 + 1.333333334 Combine like terms: -1.699673172 + 1.333333334 = -0.366339838 t = -0.366339838 Simplifying t = -0.366339838Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.033006506, -0.366339838}
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