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Simplifying 9x(x + -2) = (x + 2) Reorder the terms: 9x(-2 + x) = (x + 2) (-2 * 9x + x * 9x) = (x + 2) (-18x + 9x2) = (x + 2) Reorder the terms: -18x + 9x2 = (2 + x) Remove parenthesis around (2 + x) -18x + 9x2 = 2 + x Solving -18x + 9x2 = 2 + x Solving for variable 'x'. Reorder the terms: -2 + -18x + -1x + 9x2 = 2 + x + -2 + -1x Combine like terms: -18x + -1x = -19x -2 + -19x + 9x2 = 2 + x + -2 + -1x Reorder the terms: -2 + -19x + 9x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 -2 + -19x + 9x2 = 0 + x + -1x -2 + -19x + 9x2 = x + -1x Combine like terms: x + -1x = 0 -2 + -19x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + -2.111111111x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -2.111111111x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -2.111111111x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -2.111111111x + x2 = 0 + 0.2222222222 -2.111111111x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -2.111111111x + x2 = 0.2222222222 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 = 0.2222222222 + 1.114197532 Reorder the terms: 1.114197532 + -2.111111111x + x2 = 0.2222222222 + 1.114197532 Combine like terms: 0.2222222222 + 1.114197532 = 1.3364197542 1.114197532 + -2.111111111x + x2 = 1.3364197542 Factor a perfect square on the left side: (x + -1.055555556)(x + -1.055555556) = 1.3364197542 Calculate the square root of the right side: 1.156036225 Break this problem into two subproblems by setting (x + -1.055555556) equal to 1.156036225 and -1.156036225.Subproblem 1
x + -1.055555556 = 1.156036225 Simplifying x + -1.055555556 = 1.156036225 Reorder the terms: -1.055555556 + x = 1.156036225 Solving -1.055555556 + x = 1.156036225 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 = 1.156036225 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = 1.156036225 + 1.055555556 x = 1.156036225 + 1.055555556 Combine like terms: 1.156036225 + 1.055555556 = 2.211591781 x = 2.211591781 Simplifying x = 2.211591781Subproblem 2
x + -1.055555556 = -1.156036225 Simplifying x + -1.055555556 = -1.156036225 Reorder the terms: -1.055555556 + x = -1.156036225 Solving -1.055555556 + x = -1.156036225 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 = -1.156036225 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = -1.156036225 + 1.055555556 x = -1.156036225 + 1.055555556 Combine like terms: -1.156036225 + 1.055555556 = -0.100480669 x = -0.100480669 Simplifying x = -0.100480669Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.211591781, -0.100480669}
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