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Simplifying 1027x2 + -123x + 1 = 0 Reorder the terms: 1 + -123x + 1027x2 = 0 Solving 1 + -123x + 1027x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1027 the coefficient of the squared term: Divide each side by '1027'. 0.0009737098345 + -0.1197663096x + x2 = 0 Move the constant term to the right: Add '-0.0009737098345' to each side of the equation. 0.0009737098345 + -0.1197663096x + -0.0009737098345 + x2 = 0 + -0.0009737098345 Reorder the terms: 0.0009737098345 + -0.0009737098345 + -0.1197663096x + x2 = 0 + -0.0009737098345 Combine like terms: 0.0009737098345 + -0.0009737098345 = 0.0000000000000 0.0000000000000 + -0.1197663096x + x2 = 0 + -0.0009737098345 -0.1197663096x + x2 = 0 + -0.0009737098345 Combine like terms: 0 + -0.0009737098345 = -0.0009737098345 -0.1197663096x + x2 = -0.0009737098345 The x term is -0.1197663096x. Take half its coefficient (-0.0598831548). Square it (0.003585992229) and add it to both sides. Add '0.003585992229' to each side of the equation. -0.1197663096x + 0.003585992229 + x2 = -0.0009737098345 + 0.003585992229 Reorder the terms: 0.003585992229 + -0.1197663096x + x2 = -0.0009737098345 + 0.003585992229 Combine like terms: -0.0009737098345 + 0.003585992229 = 0.0026122823945 0.003585992229 + -0.1197663096x + x2 = 0.0026122823945 Factor a perfect square on the left side: (x + -0.0598831548)(x + -0.0598831548) = 0.0026122823945 Calculate the square root of the right side: 0.051110492 Break this problem into two subproblems by setting (x + -0.0598831548) equal to 0.051110492 and -0.051110492.Subproblem 1
x + -0.0598831548 = 0.051110492 Simplifying x + -0.0598831548 = 0.051110492 Reorder the terms: -0.0598831548 + x = 0.051110492 Solving -0.0598831548 + x = 0.051110492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0598831548' to each side of the equation. -0.0598831548 + 0.0598831548 + x = 0.051110492 + 0.0598831548 Combine like terms: -0.0598831548 + 0.0598831548 = 0.0000000000 0.0000000000 + x = 0.051110492 + 0.0598831548 x = 0.051110492 + 0.0598831548 Combine like terms: 0.051110492 + 0.0598831548 = 0.1109936468 x = 0.1109936468 Simplifying x = 0.1109936468Subproblem 2
x + -0.0598831548 = -0.051110492 Simplifying x + -0.0598831548 = -0.051110492 Reorder the terms: -0.0598831548 + x = -0.051110492 Solving -0.0598831548 + x = -0.051110492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0598831548' to each side of the equation. -0.0598831548 + 0.0598831548 + x = -0.051110492 + 0.0598831548 Combine like terms: -0.0598831548 + 0.0598831548 = 0.0000000000 0.0000000000 + x = -0.051110492 + 0.0598831548 x = -0.051110492 + 0.0598831548 Combine like terms: -0.051110492 + 0.0598831548 = 0.0087726628 x = 0.0087726628 Simplifying x = 0.0087726628Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1109936468, 0.0087726628}
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