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Simplifying -16t2 + 32t + 1 = 0 Reorder the terms: 1 + 32t + -16t2 = 0 Solving 1 + 32t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.0625 + -2t + t2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -2t + 0.0625 + t2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -2t + t2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -2t + t2 = 0 + 0.0625 -2t + t2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -2t + t2 = 0.0625 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 0.0625 + 1 Reorder the terms: 1 + -2t + t2 = 0.0625 + 1 Combine like terms: 0.0625 + 1 = 1.0625 1 + -2t + t2 = 1.0625 Factor a perfect square on the left side: (t + -1)(t + -1) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (t + -1) equal to 1.030776406 and -1.030776406.Subproblem 1
t + -1 = 1.030776406 Simplifying t + -1 = 1.030776406 Reorder the terms: -1 + t = 1.030776406 Solving -1 + t = 1.030776406 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 1.030776406 + 1 Combine like terms: -1 + 1 = 0 0 + t = 1.030776406 + 1 t = 1.030776406 + 1 Combine like terms: 1.030776406 + 1 = 2.030776406 t = 2.030776406 Simplifying t = 2.030776406Subproblem 2
t + -1 = -1.030776406 Simplifying t + -1 = -1.030776406 Reorder the terms: -1 + t = -1.030776406 Solving -1 + t = -1.030776406 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -1.030776406 + 1 Combine like terms: -1 + 1 = 0 0 + t = -1.030776406 + 1 t = -1.030776406 + 1 Combine like terms: -1.030776406 + 1 = -0.030776406 t = -0.030776406 Simplifying t = -0.030776406Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.030776406, -0.030776406}
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