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Simplifying 60 = -16t + 4.9t2 Solving 60 = -16t + 4.9t2 Solving for variable 't'. Reorder the terms: 60 + 16t + -4.9t2 = -16t + 16t + 4.9t2 + -4.9t2 Combine like terms: -16t + 16t = 0 60 + 16t + -4.9t2 = 0 + 4.9t2 + -4.9t2 60 + 16t + -4.9t2 = 4.9t2 + -4.9t2 Combine like terms: 4.9t2 + -4.9t2 = 0.0 60 + 16t + -4.9t2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -12.24489796 + -3.265306122t + t2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + -3.265306122t + 12.24489796 + t2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + -3.265306122t + t2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + -3.265306122t + t2 = 0 + 12.24489796 -3.265306122t + t2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 -3.265306122t + t2 = 12.24489796 The t term is -3.265306122t. Take half its coefficient (-1.632653061). Square it (2.665556018) and add it to both sides. Add '2.665556018' to each side of the equation. -3.265306122t + 2.665556018 + t2 = 12.24489796 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122t + t2 = 12.24489796 + 2.665556018 Combine like terms: 12.24489796 + 2.665556018 = 14.910453978 2.665556018 + -3.265306122t + t2 = 14.910453978 Factor a perfect square on the left side: (t + -1.632653061)(t + -1.632653061) = 14.910453978 Calculate the square root of the right side: 3.8614057 Break this problem into two subproblems by setting (t + -1.632653061) equal to 3.8614057 and -3.8614057.Subproblem 1
t + -1.632653061 = 3.8614057 Simplifying t + -1.632653061 = 3.8614057 Reorder the terms: -1.632653061 + t = 3.8614057 Solving -1.632653061 + t = 3.8614057 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = 3.8614057 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = 3.8614057 + 1.632653061 t = 3.8614057 + 1.632653061 Combine like terms: 3.8614057 + 1.632653061 = 5.494058761 t = 5.494058761 Simplifying t = 5.494058761Subproblem 2
t + -1.632653061 = -3.8614057 Simplifying t + -1.632653061 = -3.8614057 Reorder the terms: -1.632653061 + t = -3.8614057 Solving -1.632653061 + t = -3.8614057 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + t = -3.8614057 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + t = -3.8614057 + 1.632653061 t = -3.8614057 + 1.632653061 Combine like terms: -3.8614057 + 1.632653061 = -2.228752639 t = -2.228752639 Simplifying t = -2.228752639Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.494058761, -2.228752639}
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