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Simplifying 20 = -0.25t2 + 5t Reorder the terms: 20 = 5t + -0.25t2 Solving 20 = 5t + -0.25t2 Solving for variable 't'. Reorder the terms: 20 + -5t + 0.25t2 = 5t + -5t + -0.25t2 + 0.25t2 Combine like terms: 5t + -5t = 0 20 + -5t + 0.25t2 = 0 + -0.25t2 + 0.25t2 20 + -5t + 0.25t2 = -0.25t2 + 0.25t2 Combine like terms: -0.25t2 + 0.25t2 = 0.00 20 + -5t + 0.25t2 = 0.00 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 80 + -20t + t2 = 0 Move the constant term to the right: Add '-80' to each side of the equation. 80 + -20t + -80 + t2 = 0 + -80 Reorder the terms: 80 + -80 + -20t + t2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -20t + t2 = 0 + -80 -20t + t2 = 0 + -80 Combine like terms: 0 + -80 = -80 -20t + t2 = -80 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = -80 + 100 Reorder the terms: 100 + -20t + t2 = -80 + 100 Combine like terms: -80 + 100 = 20 100 + -20t + t2 = 20 Factor a perfect square on the left side: (t + -10)(t + -10) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (t + -10) equal to 4.472135955 and -4.472135955.Subproblem 1
t + -10 = 4.472135955 Simplifying t + -10 = 4.472135955 Reorder the terms: -10 + t = 4.472135955 Solving -10 + t = 4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 4.472135955 + 10 Combine like terms: -10 + 10 = 0 0 + t = 4.472135955 + 10 t = 4.472135955 + 10 Combine like terms: 4.472135955 + 10 = 14.472135955 t = 14.472135955 Simplifying t = 14.472135955Subproblem 2
t + -10 = -4.472135955 Simplifying t + -10 = -4.472135955 Reorder the terms: -10 + t = -4.472135955 Solving -10 + t = -4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -4.472135955 + 10 Combine like terms: -10 + 10 = 0 0 + t = -4.472135955 + 10 t = -4.472135955 + 10 Combine like terms: -4.472135955 + 10 = 5.527864045 t = 5.527864045 Simplifying t = 5.527864045Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.472135955, 5.527864045}
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