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Simplifying 18x2 + 2x + -1 = 0 Reorder the terms: -1 + 2x + 18x2 = 0 Solving -1 + 2x + 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 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 0.1111111111x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 0.1111111111x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 0.1111111111x + x2 = 0 + 0.05555555556 0.1111111111x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 0.1111111111x + x2 = 0.05555555556 The x term is 0.1111111111x. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111x + 0.003086419752 + x2 = 0.05555555556 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 0.05555555556 + 0.003086419752 Combine like terms: 0.05555555556 + 0.003086419752 = 0.058641975312 0.003086419752 + 0.1111111111x + x2 = 0.058641975312 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 0.058641975312 Calculate the square root of the right side: 0.242161052 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 0.242161052 and -0.242161052.Subproblem 1
x + 0.05555555555 = 0.242161052 Simplifying x + 0.05555555555 = 0.242161052 Reorder the terms: 0.05555555555 + x = 0.242161052 Solving 0.05555555555 + x = 0.242161052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = 0.242161052 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 0.242161052 + -0.05555555555 x = 0.242161052 + -0.05555555555 Combine like terms: 0.242161052 + -0.05555555555 = 0.18660549645 x = 0.18660549645 Simplifying x = 0.18660549645Subproblem 2
x + 0.05555555555 = -0.242161052 Simplifying x + 0.05555555555 = -0.242161052 Reorder the terms: 0.05555555555 + x = -0.242161052 Solving 0.05555555555 + x = -0.242161052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = -0.242161052 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -0.242161052 + -0.05555555555 x = -0.242161052 + -0.05555555555 Combine like terms: -0.242161052 + -0.05555555555 = -0.29771660755 x = -0.29771660755 Simplifying x = -0.29771660755Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.18660549645, -0.29771660755}
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