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Simplifying 16x2 + -21x + 2 = 0 Reorder the terms: 2 + -21x + 16x2 = 0 Solving 2 + -21x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.125 + -1.3125x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1.3125x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1.3125x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1.3125x + x2 = 0 + -0.125 -1.3125x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1.3125x + x2 = -0.125 The x term is -1.3125x. 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. -1.3125x + 0.4306640625 + x2 = -0.125 + 0.4306640625 Reorder the terms: 0.4306640625 + -1.3125x + x2 = -0.125 + 0.4306640625 Combine like terms: -0.125 + 0.4306640625 = 0.3056640625 0.4306640625 + -1.3125x + x2 = 0.3056640625 Factor a perfect square on the left side: (x + -0.65625)(x + -0.65625) = 0.3056640625 Calculate the square root of the right side: 0.552868938 Break this problem into two subproblems by setting (x + -0.65625) equal to 0.552868938 and -0.552868938.Subproblem 1
x + -0.65625 = 0.552868938 Simplifying x + -0.65625 = 0.552868938 Reorder the terms: -0.65625 + x = 0.552868938 Solving -0.65625 + x = 0.552868938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + x = 0.552868938 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = 0.552868938 + 0.65625 x = 0.552868938 + 0.65625 Combine like terms: 0.552868938 + 0.65625 = 1.209118938 x = 1.209118938 Simplifying x = 1.209118938Subproblem 2
x + -0.65625 = -0.552868938 Simplifying x + -0.65625 = -0.552868938 Reorder the terms: -0.65625 + x = -0.552868938 Solving -0.65625 + x = -0.552868938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.65625' to each side of the equation. -0.65625 + 0.65625 + x = -0.552868938 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + x = -0.552868938 + 0.65625 x = -0.552868938 + 0.65625 Combine like terms: -0.552868938 + 0.65625 = 0.103381062 x = 0.103381062 Simplifying x = 0.103381062Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.209118938, 0.103381062}
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