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Simplifying 0 = -16t2 + 56t + 1 Reorder the terms: 0 = 1 + 56t + -16t2 Solving 0 = 1 + 56t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1 = -1 -1 + -56t + 16t2 = 1 + 56t + -16t2 + -1 + -56t + 16t2 Reorder the terms: -1 + -56t + 16t2 = 1 + -1 + 56t + -56t + -16t2 + 16t2 Combine like terms: 1 + -1 = 0 -1 + -56t + 16t2 = 0 + 56t + -56t + -16t2 + 16t2 -1 + -56t + 16t2 = 56t + -56t + -16t2 + 16t2 Combine like terms: 56t + -56t = 0 -1 + -56t + 16t2 = 0 + -16t2 + 16t2 -1 + -56t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1 + -56t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -3.5t + t2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -3.5t + 0.0625 + t2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -3.5t + t2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -3.5t + t2 = 0 + 0.0625 -3.5t + t2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -3.5t + t2 = 0.0625 The t term is -3.5t. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5t + 3.0625 + t2 = 0.0625 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = 0.0625 + 3.0625 Combine like terms: 0.0625 + 3.0625 = 3.125 3.0625 + -3.5t + t2 = 3.125 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (t + -1.75) equal to 1.767766953 and -1.767766953.Subproblem 1
t + -1.75 = 1.767766953 Simplifying t + -1.75 = 1.767766953 Reorder the terms: -1.75 + t = 1.767766953 Solving -1.75 + t = 1.767766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = 1.767766953 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 1.767766953 + 1.75 t = 1.767766953 + 1.75 Combine like terms: 1.767766953 + 1.75 = 3.517766953 t = 3.517766953 Simplifying t = 3.517766953Subproblem 2
t + -1.75 = -1.767766953 Simplifying t + -1.75 = -1.767766953 Reorder the terms: -1.75 + t = -1.767766953 Solving -1.75 + t = -1.767766953 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = -1.767766953 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -1.767766953 + 1.75 t = -1.767766953 + 1.75 Combine like terms: -1.767766953 + 1.75 = -0.017766953 t = -0.017766953 Simplifying t = -0.017766953Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.517766953, -0.017766953}
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