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Simplifying 0 = -16t2 + 64t + 3 Reorder the terms: 0 = 3 + 64t + -16t2 Solving 0 = 3 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -3 = -3 -3 + -64t + 16t2 = 3 + 64t + -16t2 + -3 + -64t + 16t2 Reorder the terms: -3 + -64t + 16t2 = 3 + -3 + 64t + -64t + -16t2 + 16t2 Combine like terms: 3 + -3 = 0 -3 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -3 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -3 + -64t + 16t2 = 0 + -16t2 + 16t2 -3 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -3 + -64t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + -4t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -4t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -4t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -4t + t2 = 0 + 0.1875 -4t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -4t + t2 = 0.1875 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 = 0.1875 + 4 Reorder the terms: 4 + -4t + t2 = 0.1875 + 4 Combine like terms: 0.1875 + 4 = 4.1875 4 + -4t + t2 = 4.1875 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.1875 Calculate the square root of the right side: 2.046338193 Break this problem into two subproblems by setting (t + -2) equal to 2.046338193 and -2.046338193.Subproblem 1
t + -2 = 2.046338193 Simplifying t + -2 = 2.046338193 Reorder the terms: -2 + t = 2.046338193 Solving -2 + t = 2.046338193 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 = 2.046338193 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.046338193 + 2 t = 2.046338193 + 2 Combine like terms: 2.046338193 + 2 = 4.046338193 t = 4.046338193 Simplifying t = 4.046338193Subproblem 2
t + -2 = -2.046338193 Simplifying t + -2 = -2.046338193 Reorder the terms: -2 + t = -2.046338193 Solving -2 + t = -2.046338193 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 = -2.046338193 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.046338193 + 2 t = -2.046338193 + 2 Combine like terms: -2.046338193 + 2 = -0.046338193 t = -0.046338193 Simplifying t = -0.046338193Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.046338193, -0.046338193}
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