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Simplifying x2 + -2x + 0.48 = 0 Reorder the terms: 0.48 + -2x + x2 = 0 Solving 0.48 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.48' to each side of the equation. 0.48 + -2x + -0.48 + x2 = 0 + -0.48 Reorder the terms: 0.48 + -0.48 + -2x + x2 = 0 + -0.48 Combine like terms: 0.48 + -0.48 = 0.00 0.00 + -2x + x2 = 0 + -0.48 -2x + x2 = 0 + -0.48 Combine like terms: 0 + -0.48 = -0.48 -2x + x2 = -0.48 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.48 + 1 Reorder the terms: 1 + -2x + x2 = -0.48 + 1 Combine like terms: -0.48 + 1 = 0.52 1 + -2x + x2 = 0.52 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.52 Calculate the square root of the right side: 0.721110255 Break this problem into two subproblems by setting (x + -1) equal to 0.721110255 and -0.721110255.Subproblem 1
x + -1 = 0.721110255 Simplifying x + -1 = 0.721110255 Reorder the terms: -1 + x = 0.721110255 Solving -1 + x = 0.721110255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.721110255 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.721110255 + 1 x = 0.721110255 + 1 Combine like terms: 0.721110255 + 1 = 1.721110255 x = 1.721110255 Simplifying x = 1.721110255Subproblem 2
x + -1 = -0.721110255 Simplifying x + -1 = -0.721110255 Reorder the terms: -1 + x = -0.721110255 Solving -1 + x = -0.721110255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.721110255 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.721110255 + 1 x = -0.721110255 + 1 Combine like terms: -0.721110255 + 1 = 0.278889745 x = 0.278889745 Simplifying x = 0.278889745Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.721110255, 0.278889745}
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