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Simplifying 0 = -15t2 + 44t + -24 Reorder the terms: 0 = -24 + 44t + -15t2 Solving 0 = -24 + 44t + -15t2 Solving for variable 't'. Combine like terms: 0 + 24 = 24 24 + -44t + 15t2 = -24 + 44t + -15t2 + 24 + -44t + 15t2 Reorder the terms: 24 + -44t + 15t2 = -24 + 24 + 44t + -44t + -15t2 + 15t2 Combine like terms: -24 + 24 = 0 24 + -44t + 15t2 = 0 + 44t + -44t + -15t2 + 15t2 24 + -44t + 15t2 = 44t + -44t + -15t2 + 15t2 Combine like terms: 44t + -44t = 0 24 + -44t + 15t2 = 0 + -15t2 + 15t2 24 + -44t + 15t2 = -15t2 + 15t2 Combine like terms: -15t2 + 15t2 = 0 24 + -44t + 15t2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 1.6 + -2.933333333t + t2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -2.933333333t + -1.6 + t2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -2.933333333t + t2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -2.933333333t + t2 = 0 + -1.6 -2.933333333t + t2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -2.933333333t + t2 = -1.6 The t term is -2.933333333t. Take half its coefficient (-1.466666667). Square it (2.151111112) and add it to both sides. Add '2.151111112' to each side of the equation. -2.933333333t + 2.151111112 + t2 = -1.6 + 2.151111112 Reorder the terms: 2.151111112 + -2.933333333t + t2 = -1.6 + 2.151111112 Combine like terms: -1.6 + 2.151111112 = 0.551111112 2.151111112 + -2.933333333t + t2 = 0.551111112 Factor a perfect square on the left side: (t + -1.466666667)(t + -1.466666667) = 0.551111112 Calculate the square root of the right side: 0.742368582 Break this problem into two subproblems by setting (t + -1.466666667) equal to 0.742368582 and -0.742368582.Subproblem 1
t + -1.466666667 = 0.742368582 Simplifying t + -1.466666667 = 0.742368582 Reorder the terms: -1.466666667 + t = 0.742368582 Solving -1.466666667 + t = 0.742368582 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.466666667' to each side of the equation. -1.466666667 + 1.466666667 + t = 0.742368582 + 1.466666667 Combine like terms: -1.466666667 + 1.466666667 = 0.000000000 0.000000000 + t = 0.742368582 + 1.466666667 t = 0.742368582 + 1.466666667 Combine like terms: 0.742368582 + 1.466666667 = 2.209035249 t = 2.209035249 Simplifying t = 2.209035249Subproblem 2
t + -1.466666667 = -0.742368582 Simplifying t + -1.466666667 = -0.742368582 Reorder the terms: -1.466666667 + t = -0.742368582 Solving -1.466666667 + t = -0.742368582 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.466666667' to each side of the equation. -1.466666667 + 1.466666667 + t = -0.742368582 + 1.466666667 Combine like terms: -1.466666667 + 1.466666667 = 0.000000000 0.000000000 + t = -0.742368582 + 1.466666667 t = -0.742368582 + 1.466666667 Combine like terms: -0.742368582 + 1.466666667 = 0.724298085 t = 0.724298085 Simplifying t = 0.724298085Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.209035249, 0.724298085}
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