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Simplifying 16t2 + -56t + -5 = 0 Reorder the terms: -5 + -56t + 16t2 = 0 Solving -5 + -56t + 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'. -0.3125 + -3.5t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -3.5t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -3.5t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -3.5t + t2 = 0 + 0.3125 -3.5t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -3.5t + t2 = 0.3125 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 = 0.3125 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = 0.3125 + 3.0625 Combine like terms: 0.3125 + 3.0625 = 3.375 3.0625 + -3.5t + t2 = 3.375 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = 3.375 Calculate the square root of the right side: 1.837117307 Break this problem into two subproblems by setting (t + -1.75) equal to 1.837117307 and -1.837117307.Subproblem 1
t + -1.75 = 1.837117307 Simplifying t + -1.75 = 1.837117307 Reorder the terms: -1.75 + t = 1.837117307 Solving -1.75 + t = 1.837117307 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 = 1.837117307 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 1.837117307 + 1.75 t = 1.837117307 + 1.75 Combine like terms: 1.837117307 + 1.75 = 3.587117307 t = 3.587117307 Simplifying t = 3.587117307Subproblem 2
t + -1.75 = -1.837117307 Simplifying t + -1.75 = -1.837117307 Reorder the terms: -1.75 + t = -1.837117307 Solving -1.75 + t = -1.837117307 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 = -1.837117307 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -1.837117307 + 1.75 t = -1.837117307 + 1.75 Combine like terms: -1.837117307 + 1.75 = -0.087117307 t = -0.087117307 Simplifying t = -0.087117307Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.587117307, -0.087117307}
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