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Simplifying 16t2 + -21t + 2 = 0 Reorder the terms: 2 + -21t + 16t2 = 0 Solving 2 + -21t + 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'. 0.125 + -1.3125t + t2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1.3125t + -0.125 + t2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1.3125t + t2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1.3125t + t2 = 0 + -0.125 -1.3125t + t2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1.3125t + t2 = -0.125 The t term is -1.3125t. Take half its coefficient (-0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. -1.3125t + 0.4306640625 + t2 = -0.125 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125t + t2 = -0.125 + 0.4306640625 Combine like terms: -0.125 + 0.4306640625 = 0.3056640625 0.4306640625 + -1.3125t + t2 = 0.3056640625 Factor a perfect square on the left side: (t + -0.65625)(t + -0.65625) = 0.3056640625 Calculate the square root of the right side: 0.552868938 Break this problem into two subproblems by setting (t + -0.65625) equal to 0.552868938 and -0.552868938.Subproblem 1
t + -0.65625 = 0.552868938 Simplifying t + -0.65625 = 0.552868938 Reorder the terms: -0.65625 + t = 0.552868938 Solving -0.65625 + t = 0.552868938 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + t = 0.552868938 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + t = 0.552868938 + 0.65625 t = 0.552868938 + 0.65625 Combine like terms: 0.552868938 + 0.65625 = 1.209118938 t = 1.209118938 Simplifying t = 1.209118938Subproblem 2
t + -0.65625 = -0.552868938 Simplifying t + -0.65625 = -0.552868938 Reorder the terms: -0.65625 + t = -0.552868938 Solving -0.65625 + t = -0.552868938 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + t = -0.552868938 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + t = -0.552868938 + 0.65625 t = -0.552868938 + 0.65625 Combine like terms: -0.552868938 + 0.65625 = 0.103381062 t = 0.103381062 Simplifying t = 0.103381062Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.209118938, 0.103381062}
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