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Simplifying -0.483x2 + 0.263x + -0.0109 = 0 Reorder the terms: -0.0109 + 0.263x + -0.483x2 = 0 Solving -0.0109 + 0.263x + -0.483x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.483 the coefficient of the squared term: Divide each side by '-0.483'. 0.02256728778 + -0.5445134576x + x2 = 0 Move the constant term to the right: Add '-0.02256728778' to each side of the equation. 0.02256728778 + -0.5445134576x + -0.02256728778 + x2 = 0 + -0.02256728778 Reorder the terms: 0.02256728778 + -0.02256728778 + -0.5445134576x + x2 = 0 + -0.02256728778 Combine like terms: 0.02256728778 + -0.02256728778 = 0.00000000000 0.00000000000 + -0.5445134576x + x2 = 0 + -0.02256728778 -0.5445134576x + x2 = 0 + -0.02256728778 Combine like terms: 0 + -0.02256728778 = -0.02256728778 -0.5445134576x + x2 = -0.02256728778 The x term is -0.5445134576x. Take half its coefficient (-0.2722567288). Square it (0.07412372638) and add it to both sides. Add '0.07412372638' to each side of the equation. -0.5445134576x + 0.07412372638 + x2 = -0.02256728778 + 0.07412372638 Reorder the terms: 0.07412372638 + -0.5445134576x + x2 = -0.02256728778 + 0.07412372638 Combine like terms: -0.02256728778 + 0.07412372638 = 0.0515564386 0.07412372638 + -0.5445134576x + x2 = 0.0515564386 Factor a perfect square on the left side: (x + -0.2722567288)(x + -0.2722567288) = 0.0515564386 Calculate the square root of the right side: 0.227060429 Break this problem into two subproblems by setting (x + -0.2722567288) equal to 0.227060429 and -0.227060429.Subproblem 1
x + -0.2722567288 = 0.227060429 Simplifying x + -0.2722567288 = 0.227060429 Reorder the terms: -0.2722567288 + x = 0.227060429 Solving -0.2722567288 + x = 0.227060429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2722567288' to each side of the equation. -0.2722567288 + 0.2722567288 + x = 0.227060429 + 0.2722567288 Combine like terms: -0.2722567288 + 0.2722567288 = 0.0000000000 0.0000000000 + x = 0.227060429 + 0.2722567288 x = 0.227060429 + 0.2722567288 Combine like terms: 0.227060429 + 0.2722567288 = 0.4993171578 x = 0.4993171578 Simplifying x = 0.4993171578Subproblem 2
x + -0.2722567288 = -0.227060429 Simplifying x + -0.2722567288 = -0.227060429 Reorder the terms: -0.2722567288 + x = -0.227060429 Solving -0.2722567288 + x = -0.227060429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2722567288' to each side of the equation. -0.2722567288 + 0.2722567288 + x = -0.227060429 + 0.2722567288 Combine like terms: -0.2722567288 + 0.2722567288 = 0.0000000000 0.0000000000 + x = -0.227060429 + 0.2722567288 x = -0.227060429 + 0.2722567288 Combine like terms: -0.227060429 + 0.2722567288 = 0.0451962998 x = 0.0451962998 Simplifying x = 0.0451962998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4993171578, 0.0451962998}
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