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Simplifying 18x2 + -198x + 1 = 0 Reorder the terms: 1 + -198x + 18x2 = 0 Solving 1 + -198x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.05555555556 + -11x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + -11x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + -11x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + -11x + x2 = 0 + -0.05555555556 -11x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 -11x + x2 = -0.05555555556 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -0.05555555556 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -0.05555555556 + 30.25 Combine like terms: -0.05555555556 + 30.25 = 30.19444444444 30.25 + -11x + x2 = 30.19444444444 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 30.19444444444 Calculate the square root of the right side: 5.494947174 Break this problem into two subproblems by setting (x + -5.5) equal to 5.494947174 and -5.494947174.Subproblem 1
x + -5.5 = 5.494947174 Simplifying x + -5.5 = 5.494947174 Reorder the terms: -5.5 + x = 5.494947174 Solving -5.5 + x = 5.494947174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.494947174 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.494947174 + 5.5 x = 5.494947174 + 5.5 Combine like terms: 5.494947174 + 5.5 = 10.994947174 x = 10.994947174 Simplifying x = 10.994947174Subproblem 2
x + -5.5 = -5.494947174 Simplifying x + -5.5 = -5.494947174 Reorder the terms: -5.5 + x = -5.494947174 Solving -5.5 + x = -5.494947174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.494947174 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.494947174 + 5.5 x = -5.494947174 + 5.5 Combine like terms: -5.494947174 + 5.5 = 0.005052826 x = 0.005052826 Simplifying x = 0.005052826Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.994947174, 0.005052826}
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