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Simplifying 0 = -5t2 + 24t + -20 Reorder the terms: 0 = -20 + 24t + -5t2 Solving 0 = -20 + 24t + -5t2 Solving for variable 't'. Combine like terms: 0 + 20 = 20 20 + -24t + 5t2 = -20 + 24t + -5t2 + 20 + -24t + 5t2 Reorder the terms: 20 + -24t + 5t2 = -20 + 20 + 24t + -24t + -5t2 + 5t2 Combine like terms: -20 + 20 = 0 20 + -24t + 5t2 = 0 + 24t + -24t + -5t2 + 5t2 20 + -24t + 5t2 = 24t + -24t + -5t2 + 5t2 Combine like terms: 24t + -24t = 0 20 + -24t + 5t2 = 0 + -5t2 + 5t2 20 + -24t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 20 + -24t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 4 + -4.8t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -4.8t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -4.8t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -4.8t + t2 = 0 + -4 -4.8t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -4.8t + t2 = -4 The t term is -4.8t. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8t + 5.76 + t2 = -4 + 5.76 Reorder the terms: 5.76 + -4.8t + t2 = -4 + 5.76 Combine like terms: -4 + 5.76 = 1.76 5.76 + -4.8t + t2 = 1.76 Factor a perfect square on the left side: (t + -2.4)(t + -2.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (t + -2.4) equal to 1.326649916 and -1.326649916.Subproblem 1
t + -2.4 = 1.326649916 Simplifying t + -2.4 = 1.326649916 Reorder the terms: -2.4 + t = 1.326649916 Solving -2.4 + t = 1.326649916 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + t = 1.326649916 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + t = 1.326649916 + 2.4 t = 1.326649916 + 2.4 Combine like terms: 1.326649916 + 2.4 = 3.726649916 t = 3.726649916 Simplifying t = 3.726649916Subproblem 2
t + -2.4 = -1.326649916 Simplifying t + -2.4 = -1.326649916 Reorder the terms: -2.4 + t = -1.326649916 Solving -2.4 + t = -1.326649916 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + t = -1.326649916 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + t = -1.326649916 + 2.4 t = -1.326649916 + 2.4 Combine like terms: -1.326649916 + 2.4 = 1.073350084 t = 1.073350084 Simplifying t = 1.073350084Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.726649916, 1.073350084}
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