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Simplifying 18x2 + 2x + -5 = 0 Reorder the terms: -5 + 2x + 18x2 = 0 Solving -5 + 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'. -0.2777777778 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.1111111111x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + 0.1111111111x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + 0.1111111111x + x2 = 0 + 0.2777777778 0.1111111111x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 0.1111111111x + x2 = 0.2777777778 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 = 0.2777777778 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 0.2777777778 + 0.003086419752 Combine like terms: 0.2777777778 + 0.003086419752 = 0.280864197552 0.003086419752 + 0.1111111111x + x2 = 0.280864197552 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 0.280864197552 Calculate the square root of the right side: 0.529966223 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 0.529966223 and -0.529966223.Subproblem 1
x + 0.05555555555 = 0.529966223 Simplifying x + 0.05555555555 = 0.529966223 Reorder the terms: 0.05555555555 + x = 0.529966223 Solving 0.05555555555 + x = 0.529966223 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 = 0.529966223 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 0.529966223 + -0.05555555555 x = 0.529966223 + -0.05555555555 Combine like terms: 0.529966223 + -0.05555555555 = 0.47441066745 x = 0.47441066745 Simplifying x = 0.47441066745Subproblem 2
x + 0.05555555555 = -0.529966223 Simplifying x + 0.05555555555 = -0.529966223 Reorder the terms: 0.05555555555 + x = -0.529966223 Solving 0.05555555555 + x = -0.529966223 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 = -0.529966223 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -0.529966223 + -0.05555555555 x = -0.529966223 + -0.05555555555 Combine like terms: -0.529966223 + -0.05555555555 = -0.58552177855 x = -0.58552177855 Simplifying x = -0.58552177855Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.47441066745, -0.58552177855}
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