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Simplifying -5 = -16t2 + 36t Reorder the terms: -5 = 36t + -16t2 Solving -5 = 36t + -16t2 Solving for variable 't'. Reorder the terms: -5 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 -5 + -36t + 16t2 = 0 + -16t2 + 16t2 -5 + -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -5 + -36t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -2.25t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -2.25t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -2.25t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -2.25t + t2 = 0 + 0.3125 -2.25t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -2.25t + t2 = 0.3125 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = 0.3125 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = 0.3125 + 1.265625 Combine like terms: 0.3125 + 1.265625 = 1.578125 1.265625 + -2.25t + t2 = 1.578125 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 1.578125 Calculate the square root of the right side: 1.256234453 Break this problem into two subproblems by setting (t + -1.125) equal to 1.256234453 and -1.256234453.Subproblem 1
t + -1.125 = 1.256234453 Simplifying t + -1.125 = 1.256234453 Reorder the terms: -1.125 + t = 1.256234453 Solving -1.125 + t = 1.256234453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 1.256234453 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 1.256234453 + 1.125 t = 1.256234453 + 1.125 Combine like terms: 1.256234453 + 1.125 = 2.381234453 t = 2.381234453 Simplifying t = 2.381234453Subproblem 2
t + -1.125 = -1.256234453 Simplifying t + -1.125 = -1.256234453 Reorder the terms: -1.125 + t = -1.256234453 Solving -1.125 + t = -1.256234453 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -1.256234453 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -1.256234453 + 1.125 t = -1.256234453 + 1.125 Combine like terms: -1.256234453 + 1.125 = -0.131234453 t = -0.131234453 Simplifying t = -0.131234453Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.381234453, -0.131234453}
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