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Simplifying 50 = -16t2 + 64t + 5 Reorder the terms: 50 = 5 + 64t + -16t2 Solving 50 = 5 + 64t + -16t2 Solving for variable 't'. Combine like terms: 50 + -5 = 45 45 + -64t + 16t2 = 5 + 64t + -16t2 + -5 + -64t + 16t2 Reorder the terms: 45 + -64t + 16t2 = 5 + -5 + 64t + -64t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 45 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 45 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 45 + -64t + 16t2 = 0 + -16t2 + 16t2 45 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 45 + -64t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.8125 + -4t + t2 = 0 Move the constant term to the right: Add '-2.8125' to each side of the equation. 2.8125 + -4t + -2.8125 + t2 = 0 + -2.8125 Reorder the terms: 2.8125 + -2.8125 + -4t + t2 = 0 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + -4t + t2 = 0 + -2.8125 -4t + t2 = 0 + -2.8125 Combine like terms: 0 + -2.8125 = -2.8125 -4t + t2 = -2.8125 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = -2.8125 + 4 Reorder the terms: 4 + -4t + t2 = -2.8125 + 4 Combine like terms: -2.8125 + 4 = 1.1875 4 + -4t + t2 = 1.1875 Factor a perfect square on the left side: (t + -2)(t + -2) = 1.1875 Calculate the square root of the right side: 1.089724736 Break this problem into two subproblems by setting (t + -2) equal to 1.089724736 and -1.089724736.Subproblem 1
t + -2 = 1.089724736 Simplifying t + -2 = 1.089724736 Reorder the terms: -2 + t = 1.089724736 Solving -2 + t = 1.089724736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 1.089724736 + 2 Combine like terms: -2 + 2 = 0 0 + t = 1.089724736 + 2 t = 1.089724736 + 2 Combine like terms: 1.089724736 + 2 = 3.089724736 t = 3.089724736 Simplifying t = 3.089724736Subproblem 2
t + -2 = -1.089724736 Simplifying t + -2 = -1.089724736 Reorder the terms: -2 + t = -1.089724736 Solving -2 + t = -1.089724736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -1.089724736 + 2 Combine like terms: -2 + 2 = 0 0 + t = -1.089724736 + 2 t = -1.089724736 + 2 Combine like terms: -1.089724736 + 2 = 0.910275264 t = 0.910275264 Simplifying t = 0.910275264Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.089724736, 0.910275264}
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