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Simplifying 36x2 + -4x + -1 = 0 Reorder the terms: -1 + -4x + 36x2 = 0 Solving -1 + -4x + 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 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.02777777778' to each side of the equation. -0.02777777778 + -0.1111111111x + 0.02777777778 + x2 = 0 + 0.02777777778 Reorder the terms: -0.02777777778 + 0.02777777778 + -0.1111111111x + x2 = 0 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + -0.1111111111x + x2 = 0 + 0.02777777778 -0.1111111111x + x2 = 0 + 0.02777777778 Combine like terms: 0 + 0.02777777778 = 0.02777777778 -0.1111111111x + x2 = 0.02777777778 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 = 0.02777777778 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 0.02777777778 + 0.003086419752 Combine like terms: 0.02777777778 + 0.003086419752 = 0.030864197532 0.003086419752 + -0.1111111111x + x2 = 0.030864197532 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 0.030864197532 Calculate the square root of the right side: 0.175682092 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 0.175682092 and -0.175682092.Subproblem 1
x + -0.05555555555 = 0.175682092 Simplifying x + -0.05555555555 = 0.175682092 Reorder the terms: -0.05555555555 + x = 0.175682092 Solving -0.05555555555 + x = 0.175682092 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 = 0.175682092 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 0.175682092 + 0.05555555555 x = 0.175682092 + 0.05555555555 Combine like terms: 0.175682092 + 0.05555555555 = 0.23123764755 x = 0.23123764755 Simplifying x = 0.23123764755Subproblem 2
x + -0.05555555555 = -0.175682092 Simplifying x + -0.05555555555 = -0.175682092 Reorder the terms: -0.05555555555 + x = -0.175682092 Solving -0.05555555555 + x = -0.175682092 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 = -0.175682092 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -0.175682092 + 0.05555555555 x = -0.175682092 + 0.05555555555 Combine like terms: -0.175682092 + 0.05555555555 = -0.12012653645 x = -0.12012653645 Simplifying x = -0.12012653645Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.23123764755, -0.12012653645}
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