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Simplifying 9x2 + -19x + 9 = 0 Reorder the terms: 9 + -19x + 9x2 = 0 Solving 9 + -19x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1 + -2.111111111x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.111111111x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.111111111x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.111111111x + x2 = 0 + -1 -2.111111111x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.111111111x + x2 = -1 The x term is -2.111111111x. Take half its coefficient (-1.055555556). Square it (1.114197532) and add it to both sides. Add '1.114197532' to each side of the equation. -2.111111111x + 1.114197532 + x2 = -1 + 1.114197532 Reorder the terms: 1.114197532 + -2.111111111x + x2 = -1 + 1.114197532 Combine like terms: -1 + 1.114197532 = 0.114197532 1.114197532 + -2.111111111x + x2 = 0.114197532 Factor a perfect square on the left side: (x + -1.055555556)(x + -1.055555556) = 0.114197532 Calculate the square root of the right side: 0.337931253 Break this problem into two subproblems by setting (x + -1.055555556) equal to 0.337931253 and -0.337931253.Subproblem 1
x + -1.055555556 = 0.337931253 Simplifying x + -1.055555556 = 0.337931253 Reorder the terms: -1.055555556 + x = 0.337931253 Solving -1.055555556 + x = 0.337931253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.055555556' to each side of the equation. -1.055555556 + 1.055555556 + x = 0.337931253 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = 0.337931253 + 1.055555556 x = 0.337931253 + 1.055555556 Combine like terms: 0.337931253 + 1.055555556 = 1.393486809 x = 1.393486809 Simplifying x = 1.393486809Subproblem 2
x + -1.055555556 = -0.337931253 Simplifying x + -1.055555556 = -0.337931253 Reorder the terms: -1.055555556 + x = -0.337931253 Solving -1.055555556 + x = -0.337931253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.055555556' to each side of the equation. -1.055555556 + 1.055555556 + x = -0.337931253 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = -0.337931253 + 1.055555556 x = -0.337931253 + 1.055555556 Combine like terms: -0.337931253 + 1.055555556 = 0.717624303 x = 0.717624303 Simplifying x = 0.717624303Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.393486809, 0.717624303}
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