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Simplifying x4 + 4x2 + -4 = 0 Reorder the terms: -4 + 4x2 + x4 = 0 Solving -4 + 4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 4x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + 4x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4x2 + x4 = 0 + 4 4x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 4x2 + x4 = 4 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 = 4 + 4 Reorder the terms: 4 + 4x2 + x4 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4x2 + x4 = 8 Factor a perfect square on the left side: (x2 + 2)(x2 + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x2 + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
x2 + 2 = 2.828427125 Simplifying x2 + 2 = 2.828427125 Reorder the terms: 2 + x2 = 2.828427125 Solving 2 + x2 = 2.828427125 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 = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = 2.828427125 + -2 x2 = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 x2 = 0.828427125 Simplifying x2 = 0.828427125 Take the square root of each side: x = {-0.910179721, 0.910179721}Subproblem 2
x2 + 2 = -2.828427125 Simplifying x2 + 2 = -2.828427125 Reorder the terms: 2 + x2 = -2.828427125 Solving 2 + x2 = -2.828427125 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 = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x2 = -2.828427125 + -2 x2 = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 x2 = -4.828427125 Simplifying x2 = -4.828427125 Reorder the terms: 4.828427125 + x2 = -4.828427125 + 4.828427125 Combine like terms: -4.828427125 + 4.828427125 = 0.000000000 4.828427125 + 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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