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Simplifying 49x2 + -22x + 1 = 0 Reorder the terms: 1 + -22x + 49x2 = 0 Solving 1 + -22x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.02040816327 + -0.4489795918x + x2 = 0 Move the constant term to the right: Add '-0.02040816327' to each side of the equation. 0.02040816327 + -0.4489795918x + -0.02040816327 + x2 = 0 + -0.02040816327 Reorder the terms: 0.02040816327 + -0.02040816327 + -0.4489795918x + x2 = 0 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + -0.4489795918x + x2 = 0 + -0.02040816327 -0.4489795918x + x2 = 0 + -0.02040816327 Combine like terms: 0 + -0.02040816327 = -0.02040816327 -0.4489795918x + x2 = -0.02040816327 The x term is -0.4489795918x. Take half its coefficient (-0.2244897959). Square it (0.05039566846) and add it to both sides. Add '0.05039566846' to each side of the equation. -0.4489795918x + 0.05039566846 + x2 = -0.02040816327 + 0.05039566846 Reorder the terms: 0.05039566846 + -0.4489795918x + x2 = -0.02040816327 + 0.05039566846 Combine like terms: -0.02040816327 + 0.05039566846 = 0.02998750519 0.05039566846 + -0.4489795918x + x2 = 0.02998750519 Factor a perfect square on the left side: (x + -0.2244897959)(x + -0.2244897959) = 0.02998750519 Calculate the square root of the right side: 0.173169008 Break this problem into two subproblems by setting (x + -0.2244897959) equal to 0.173169008 and -0.173169008.Subproblem 1
x + -0.2244897959 = 0.173169008 Simplifying x + -0.2244897959 = 0.173169008 Reorder the terms: -0.2244897959 + x = 0.173169008 Solving -0.2244897959 + x = 0.173169008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2244897959' to each side of the equation. -0.2244897959 + 0.2244897959 + x = 0.173169008 + 0.2244897959 Combine like terms: -0.2244897959 + 0.2244897959 = 0.0000000000 0.0000000000 + x = 0.173169008 + 0.2244897959 x = 0.173169008 + 0.2244897959 Combine like terms: 0.173169008 + 0.2244897959 = 0.3976588039 x = 0.3976588039 Simplifying x = 0.3976588039Subproblem 2
x + -0.2244897959 = -0.173169008 Simplifying x + -0.2244897959 = -0.173169008 Reorder the terms: -0.2244897959 + x = -0.173169008 Solving -0.2244897959 + x = -0.173169008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2244897959' to each side of the equation. -0.2244897959 + 0.2244897959 + x = -0.173169008 + 0.2244897959 Combine like terms: -0.2244897959 + 0.2244897959 = 0.0000000000 0.0000000000 + x = -0.173169008 + 0.2244897959 x = -0.173169008 + 0.2244897959 Combine like terms: -0.173169008 + 0.2244897959 = 0.0513207879 x = 0.0513207879 Simplifying x = 0.0513207879Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3976588039, 0.0513207879}
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