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Simplifying 36x2 + -40x + 1 = 0 Reorder the terms: 1 + -40x + 36x2 = 0 Solving 1 + -40x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.02777777778 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '-0.02777777778' to each side of the equation. 0.02777777778 + -1.111111111x + -0.02777777778 + x2 = 0 + -0.02777777778 Reorder the terms: 0.02777777778 + -0.02777777778 + -1.111111111x + x2 = 0 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + -1.111111111x + x2 = 0 + -0.02777777778 -1.111111111x + x2 = 0 + -0.02777777778 Combine like terms: 0 + -0.02777777778 = -0.02777777778 -1.111111111x + x2 = -0.02777777778 The x term is -1.111111111x. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111x + 0.3086419752 + x2 = -0.02777777778 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = -0.02777777778 + 0.3086419752 Combine like terms: -0.02777777778 + 0.3086419752 = 0.28086419742 0.3086419752 + -1.111111111x + x2 = 0.28086419742 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = 0.28086419742 Calculate the square root of the right side: 0.529966223 Break this problem into two subproblems by setting (x + -0.5555555555) equal to 0.529966223 and -0.529966223.Subproblem 1
x + -0.5555555555 = 0.529966223 Simplifying x + -0.5555555555 = 0.529966223 Reorder the terms: -0.5555555555 + x = 0.529966223 Solving -0.5555555555 + x = 0.529966223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = 0.529966223 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 0.529966223 + 0.5555555555 x = 0.529966223 + 0.5555555555 Combine like terms: 0.529966223 + 0.5555555555 = 1.0855217785 x = 1.0855217785 Simplifying x = 1.0855217785Subproblem 2
x + -0.5555555555 = -0.529966223 Simplifying x + -0.5555555555 = -0.529966223 Reorder the terms: -0.5555555555 + x = -0.529966223 Solving -0.5555555555 + x = -0.529966223 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = -0.529966223 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -0.529966223 + 0.5555555555 x = -0.529966223 + 0.5555555555 Combine like terms: -0.529966223 + 0.5555555555 = 0.0255893325 x = 0.0255893325 Simplifying x = 0.0255893325Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0855217785, 0.0255893325}
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