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Simplifying 60 = -16t2 + 60t + 5 Reorder the terms: 60 = 5 + 60t + -16t2 Solving 60 = 5 + 60t + -16t2 Solving for variable 't'. Combine like terms: 60 + -5 = 55 55 + -60t + 16t2 = 5 + 60t + -16t2 + -5 + -60t + 16t2 Reorder the terms: 55 + -60t + 16t2 = 5 + -5 + 60t + -60t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 55 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2 55 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 55 + -60t + 16t2 = 0 + -16t2 + 16t2 55 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 55 + -60t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.4375 + -3.75t + t2 = 0 Move the constant term to the right: Add '-3.4375' to each side of the equation. 3.4375 + -3.75t + -3.4375 + t2 = 0 + -3.4375 Reorder the terms: 3.4375 + -3.4375 + -3.75t + t2 = 0 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + -3.75t + t2 = 0 + -3.4375 -3.75t + t2 = 0 + -3.4375 Combine like terms: 0 + -3.4375 = -3.4375 -3.75t + t2 = -3.4375 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = -3.4375 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = -3.4375 + 3.515625 Combine like terms: -3.4375 + 3.515625 = 0.078125 3.515625 + -3.75t + t2 = 0.078125 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 0.078125 Calculate the square root of the right side: 0.279508497 Break this problem into two subproblems by setting (t + -1.875) equal to 0.279508497 and -0.279508497.Subproblem 1
t + -1.875 = 0.279508497 Simplifying t + -1.875 = 0.279508497 Reorder the terms: -1.875 + t = 0.279508497 Solving -1.875 + t = 0.279508497 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 0.279508497 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 0.279508497 + 1.875 t = 0.279508497 + 1.875 Combine like terms: 0.279508497 + 1.875 = 2.154508497 t = 2.154508497 Simplifying t = 2.154508497Subproblem 2
t + -1.875 = -0.279508497 Simplifying t + -1.875 = -0.279508497 Reorder the terms: -1.875 + t = -0.279508497 Solving -1.875 + t = -0.279508497 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -0.279508497 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -0.279508497 + 1.875 t = -0.279508497 + 1.875 Combine like terms: -0.279508497 + 1.875 = 1.595491503 t = 1.595491503 Simplifying t = 1.595491503Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.154508497, 1.595491503}
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