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Simplifying 9x4 + -36x2 + -8 = 0 Reorder the terms: -8 + -36x2 + 9x4 = 0 Solving -8 + -36x2 + 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'. -0.8888888889 + -4x2 + x4 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -4x2 + 0.8888888889 + x4 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -4x2 + x4 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -4x2 + x4 = 0 + 0.8888888889 -4x2 + x4 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -4x2 + x4 = 0.8888888889 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = 0.8888888889 + 4 Reorder the terms: 4 + -4x2 + x4 = 0.8888888889 + 4 Combine like terms: 0.8888888889 + 4 = 4.8888888889 4 + -4x2 + x4 = 4.8888888889 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 4.8888888889 Calculate the square root of the right side: 2.211083194 Break this problem into two subproblems by setting (x2 + -2) equal to 2.211083194 and -2.211083194.Subproblem 1
x2 + -2 = 2.211083194 Simplifying x2 + -2 = 2.211083194 Reorder the terms: -2 + x2 = 2.211083194 Solving -2 + x2 = 2.211083194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 2.211083194 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.211083194 + 2 x2 = 2.211083194 + 2 Combine like terms: 2.211083194 + 2 = 4.211083194 x2 = 4.211083194 Simplifying x2 = 4.211083194 Take the square root of each side: x = {-2.052092394, 2.052092394}Subproblem 2
x2 + -2 = -2.211083194 Simplifying x2 + -2 = -2.211083194 Reorder the terms: -2 + x2 = -2.211083194 Solving -2 + x2 = -2.211083194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -2.211083194 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.211083194 + 2 x2 = -2.211083194 + 2 Combine like terms: -2.211083194 + 2 = -0.211083194 x2 = -0.211083194 Simplifying x2 = -0.211083194 Reorder the terms: 0.211083194 + x2 = -0.211083194 + 0.211083194 Combine like terms: -0.211083194 + 0.211083194 = 0.000000000 0.211083194 + 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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