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Simplifying 23x2 + -22x + 1 = 0 Reorder the terms: 1 + -22x + 23x2 = 0 Solving 1 + -22x + 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 + -0.9565217391x + x2 = 0 Move the constant term to the right: Add '-0.04347826087' to each side of the equation. 0.04347826087 + -0.9565217391x + -0.04347826087 + x2 = 0 + -0.04347826087 Reorder the terms: 0.04347826087 + -0.04347826087 + -0.9565217391x + x2 = 0 + -0.04347826087 Combine like terms: 0.04347826087 + -0.04347826087 = 0.00000000000 0.00000000000 + -0.9565217391x + x2 = 0 + -0.04347826087 -0.9565217391x + x2 = 0 + -0.04347826087 Combine like terms: 0 + -0.04347826087 = -0.04347826087 -0.9565217391x + x2 = -0.04347826087 The x term is -0.9565217391x. Take half its coefficient (-0.4782608696). Square it (0.2287334594) and add it to both sides. Add '0.2287334594' to each side of the equation. -0.9565217391x + 0.2287334594 + x2 = -0.04347826087 + 0.2287334594 Reorder the terms: 0.2287334594 + -0.9565217391x + x2 = -0.04347826087 + 0.2287334594 Combine like terms: -0.04347826087 + 0.2287334594 = 0.18525519853 0.2287334594 + -0.9565217391x + x2 = 0.18525519853 Factor a perfect square on the left side: (x + -0.4782608696)(x + -0.4782608696) = 0.18525519853 Calculate the square root of the right side: 0.430412823 Break this problem into two subproblems by setting (x + -0.4782608696) equal to 0.430412823 and -0.430412823.Subproblem 1
x + -0.4782608696 = 0.430412823 Simplifying x + -0.4782608696 = 0.430412823 Reorder the terms: -0.4782608696 + x = 0.430412823 Solving -0.4782608696 + x = 0.430412823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4782608696' to each side of the equation. -0.4782608696 + 0.4782608696 + x = 0.430412823 + 0.4782608696 Combine like terms: -0.4782608696 + 0.4782608696 = 0.0000000000 0.0000000000 + x = 0.430412823 + 0.4782608696 x = 0.430412823 + 0.4782608696 Combine like terms: 0.430412823 + 0.4782608696 = 0.9086736926 x = 0.9086736926 Simplifying x = 0.9086736926Subproblem 2
x + -0.4782608696 = -0.430412823 Simplifying x + -0.4782608696 = -0.430412823 Reorder the terms: -0.4782608696 + x = -0.430412823 Solving -0.4782608696 + x = -0.430412823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4782608696' to each side of the equation. -0.4782608696 + 0.4782608696 + x = -0.430412823 + 0.4782608696 Combine like terms: -0.4782608696 + 0.4782608696 = 0.0000000000 0.0000000000 + x = -0.430412823 + 0.4782608696 x = -0.430412823 + 0.4782608696 Combine like terms: -0.430412823 + 0.4782608696 = 0.0478480466 x = 0.0478480466 Simplifying x = 0.0478480466Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9086736926, 0.0478480466}
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