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Simplifying 0 = -16t2 + 4t + 25 Reorder the terms: 0 = 25 + 4t + -16t2 Solving 0 = 25 + 4t + -16t2 Solving for variable 't'. Combine like terms: 0 + -25 = -25 -25 + -4t + 16t2 = 25 + 4t + -16t2 + -25 + -4t + 16t2 Reorder the terms: -25 + -4t + 16t2 = 25 + -25 + 4t + -4t + -16t2 + 16t2 Combine like terms: 25 + -25 = 0 -25 + -4t + 16t2 = 0 + 4t + -4t + -16t2 + 16t2 -25 + -4t + 16t2 = 4t + -4t + -16t2 + 16t2 Combine like terms: 4t + -4t = 0 -25 + -4t + 16t2 = 0 + -16t2 + 16t2 -25 + -4t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -25 + -4t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.5625 + -0.25t + t2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -0.25t + 1.5625 + t2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -0.25t + t2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -0.25t + t2 = 0 + 1.5625 -0.25t + t2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -0.25t + t2 = 1.5625 The t term is -0.25t. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25t + 0.015625 + t2 = 1.5625 + 0.015625 Reorder the terms: 0.015625 + -0.25t + t2 = 1.5625 + 0.015625 Combine like terms: 1.5625 + 0.015625 = 1.578125 0.015625 + -0.25t + t2 = 1.578125 Factor a perfect square on the left side: (t + -0.125)(t + -0.125) = 1.578125 Calculate the square root of the right side: 1.256234453 Break this problem into two subproblems by setting (t + -0.125) equal to 1.256234453 and -1.256234453.Subproblem 1
t + -0.125 = 1.256234453 Simplifying t + -0.125 = 1.256234453 Reorder the terms: -0.125 + t = 1.256234453 Solving -0.125 + t = 1.256234453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = 1.256234453 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = 1.256234453 + 0.125 t = 1.256234453 + 0.125 Combine like terms: 1.256234453 + 0.125 = 1.381234453 t = 1.381234453 Simplifying t = 1.381234453Subproblem 2
t + -0.125 = -1.256234453 Simplifying t + -0.125 = -1.256234453 Reorder the terms: -0.125 + t = -1.256234453 Solving -0.125 + t = -1.256234453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + t = -1.256234453 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + t = -1.256234453 + 0.125 t = -1.256234453 + 0.125 Combine like terms: -1.256234453 + 0.125 = -1.131234453 t = -1.131234453 Simplifying t = -1.131234453Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.381234453, -1.131234453}
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