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Simplifying 9x4 + -19x2 + -2 = 0 Reorder the terms: -2 + -19x2 + 9x4 = 0 Solving -2 + -19x2 + 9x4 = 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'. -0.2222222222 + -2.111111111x2 + x4 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -2.111111111x2 + 0.2222222222 + x4 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -2.111111111x2 + x4 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -2.111111111x2 + x4 = 0 + 0.2222222222 -2.111111111x2 + x4 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -2.111111111x2 + x4 = 0.2222222222 The x term is -2.111111111x2. 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. -2.111111111x2 + 1.114197532 + x4 = 0.2222222222 + 1.114197532 Reorder the terms: 1.114197532 + -2.111111111x2 + x4 = 0.2222222222 + 1.114197532 Combine like terms: 0.2222222222 + 1.114197532 = 1.3364197542 1.114197532 + -2.111111111x2 + x4 = 1.3364197542 Factor a perfect square on the left side: (x2 + -1.055555556)(x2 + -1.055555556) = 1.3364197542 Calculate the square root of the right side: 1.156036225 Break this problem into two subproblems by setting (x2 + -1.055555556) equal to 1.156036225 and -1.156036225.Subproblem 1
x2 + -1.055555556 = 1.156036225 Simplifying x2 + -1.055555556 = 1.156036225 Reorder the terms: -1.055555556 + x2 = 1.156036225 Solving -1.055555556 + x2 = 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 + x2 = 1.156036225 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x2 = 1.156036225 + 1.055555556 x2 = 1.156036225 + 1.055555556 Combine like terms: 1.156036225 + 1.055555556 = 2.211591781 x2 = 2.211591781 Simplifying x2 = 2.211591781 Take the square root of each side: x = {-1.487142152, 1.487142152}Subproblem 2
x2 + -1.055555556 = -1.156036225 Simplifying x2 + -1.055555556 = -1.156036225 Reorder the terms: -1.055555556 + x2 = -1.156036225 Solving -1.055555556 + x2 = -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 + x2 = -1.156036225 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x2 = -1.156036225 + 1.055555556 x2 = -1.156036225 + 1.055555556 Combine like terms: -1.156036225 + 1.055555556 = -0.100480669 x2 = -0.100480669 Simplifying x2 = -0.100480669 Reorder the terms: 0.100480669 + x2 = -0.100480669 + 0.100480669 Combine like terms: -0.100480669 + 0.100480669 = 0.000000000 0.100480669 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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