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Simplifying 23x2 + -10x + 1 = 0 Reorder the terms: 1 + -10x + 23x2 = 0 Solving 1 + -10x + 23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. 0.04347826087 + -0.4347826087x + x2 = 0 Move the constant term to the right: Add '-0.04347826087' to each side of the equation. 0.04347826087 + -0.4347826087x + -0.04347826087 + x2 = 0 + -0.04347826087 Reorder the terms: 0.04347826087 + -0.04347826087 + -0.4347826087x + x2 = 0 + -0.04347826087 Combine like terms: 0.04347826087 + -0.04347826087 = 0.00000000000 0.00000000000 + -0.4347826087x + x2 = 0 + -0.04347826087 -0.4347826087x + x2 = 0 + -0.04347826087 Combine like terms: 0 + -0.04347826087 = -0.04347826087 -0.4347826087x + x2 = -0.04347826087 The x term is -0.4347826087x. Take half its coefficient (-0.2173913044). Square it (0.04725897923) and add it to both sides. Add '0.04725897923' to each side of the equation. -0.4347826087x + 0.04725897923 + x2 = -0.04347826087 + 0.04725897923 Reorder the terms: 0.04725897923 + -0.4347826087x + x2 = -0.04347826087 + 0.04725897923 Combine like terms: -0.04347826087 + 0.04725897923 = 0.00378071836 0.04725897923 + -0.4347826087x + x2 = 0.00378071836 Factor a perfect square on the left side: (x + -0.2173913044)(x + -0.2173913044) = 0.00378071836 Calculate the square root of the right side: 0.061487546 Break this problem into two subproblems by setting (x + -0.2173913044) equal to 0.061487546 and -0.061487546.Subproblem 1
x + -0.2173913044 = 0.061487546 Simplifying x + -0.2173913044 = 0.061487546 Reorder the terms: -0.2173913044 + x = 0.061487546 Solving -0.2173913044 + x = 0.061487546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2173913044' to each side of the equation. -0.2173913044 + 0.2173913044 + x = 0.061487546 + 0.2173913044 Combine like terms: -0.2173913044 + 0.2173913044 = 0.0000000000 0.0000000000 + x = 0.061487546 + 0.2173913044 x = 0.061487546 + 0.2173913044 Combine like terms: 0.061487546 + 0.2173913044 = 0.2788788504 x = 0.2788788504 Simplifying x = 0.2788788504Subproblem 2
x + -0.2173913044 = -0.061487546 Simplifying x + -0.2173913044 = -0.061487546 Reorder the terms: -0.2173913044 + x = -0.061487546 Solving -0.2173913044 + x = -0.061487546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2173913044' to each side of the equation. -0.2173913044 + 0.2173913044 + x = -0.061487546 + 0.2173913044 Combine like terms: -0.2173913044 + 0.2173913044 = 0.0000000000 0.0000000000 + x = -0.061487546 + 0.2173913044 x = -0.061487546 + 0.2173913044 Combine like terms: -0.061487546 + 0.2173913044 = 0.1559037584 x = 0.1559037584 Simplifying x = 0.1559037584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2788788504, 0.1559037584}
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