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Simplifying 16t2 + -56t + 35 = 0 Reorder the terms: 35 + -56t + 16t2 = 0 Solving 35 + -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'. 2.1875 + -3.5t + t2 = 0 Move the constant term to the right: Add '-2.1875' to each side of the equation. 2.1875 + -3.5t + -2.1875 + t2 = 0 + -2.1875 Reorder the terms: 2.1875 + -2.1875 + -3.5t + t2 = 0 + -2.1875 Combine like terms: 2.1875 + -2.1875 = 0.0000 0.0000 + -3.5t + t2 = 0 + -2.1875 -3.5t + t2 = 0 + -2.1875 Combine like terms: 0 + -2.1875 = -2.1875 -3.5t + t2 = -2.1875 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 = -2.1875 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = -2.1875 + 3.0625 Combine like terms: -2.1875 + 3.0625 = 0.875 3.0625 + -3.5t + t2 = 0.875 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (t + -1.75) equal to 0.935414347 and -0.935414347.Subproblem 1
t + -1.75 = 0.935414347 Simplifying t + -1.75 = 0.935414347 Reorder the terms: -1.75 + t = 0.935414347 Solving -1.75 + t = 0.935414347 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 = 0.935414347 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 0.935414347 + 1.75 t = 0.935414347 + 1.75 Combine like terms: 0.935414347 + 1.75 = 2.685414347 t = 2.685414347 Simplifying t = 2.685414347Subproblem 2
t + -1.75 = -0.935414347 Simplifying t + -1.75 = -0.935414347 Reorder the terms: -1.75 + t = -0.935414347 Solving -1.75 + t = -0.935414347 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 = -0.935414347 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -0.935414347 + 1.75 t = -0.935414347 + 1.75 Combine like terms: -0.935414347 + 1.75 = 0.814585653 t = 0.814585653 Simplifying t = 0.814585653Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.685414347, 0.814585653}
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