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Simplifying 0 = -16t2 + -64t + 5 Reorder the terms: 0 = 5 + -64t + -16t2 Solving 0 = 5 + -64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + 64t + 16t2 = 5 + -64t + -16t2 + -5 + 64t + 16t2 Reorder the terms: -5 + 64t + 16t2 = 5 + -5 + -64t + 64t + -16t2 + 16t2 Combine like terms: 5 + -5 = 0 -5 + 64t + 16t2 = 0 + -64t + 64t + -16t2 + 16t2 -5 + 64t + 16t2 = -64t + 64t + -16t2 + 16t2 Combine like terms: -64t + 64t = 0 -5 + 64t + 16t2 = 0 + -16t2 + 16t2 -5 + 64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + 64t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + 4t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 4t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 4t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 4t + t2 = 0 + 0.3125 4t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 4t + t2 = 0.3125 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 = 0.3125 + 4 Reorder the terms: 4 + 4t + t2 = 0.3125 + 4 Combine like terms: 0.3125 + 4 = 4.3125 4 + 4t + t2 = 4.3125 Factor a perfect square on the left side: (t + 2)(t + 2) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (t + 2) equal to 2.076655966 and -2.076655966.Subproblem 1
t + 2 = 2.076655966 Simplifying t + 2 = 2.076655966 Reorder the terms: 2 + t = 2.076655966 Solving 2 + t = 2.076655966 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 = 2.076655966 + -2 Combine like terms: 2 + -2 = 0 0 + t = 2.076655966 + -2 t = 2.076655966 + -2 Combine like terms: 2.076655966 + -2 = 0.076655966 t = 0.076655966 Simplifying t = 0.076655966Subproblem 2
t + 2 = -2.076655966 Simplifying t + 2 = -2.076655966 Reorder the terms: 2 + t = -2.076655966 Solving 2 + t = -2.076655966 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 = -2.076655966 + -2 Combine like terms: 2 + -2 = 0 0 + t = -2.076655966 + -2 t = -2.076655966 + -2 Combine like terms: -2.076655966 + -2 = -4.076655966 t = -4.076655966 Simplifying t = -4.076655966Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.076655966, -4.076655966}
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