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Simplifying x4 + -8x2 + -32 = 0 Reorder the terms: -32 + -8x2 + x4 = 0 Solving -32 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -8x2 + 32 + x4 = 0 + 32 Reorder the terms: -32 + 32 + -8x2 + x4 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -8x2 + x4 = 0 + 32 -8x2 + x4 = 0 + 32 Combine like terms: 0 + 32 = 32 -8x2 + x4 = 32 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = 32 + 16 Reorder the terms: 16 + -8x2 + x4 = 32 + 16 Combine like terms: 32 + 16 = 48 16 + -8x2 + x4 = 48 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x2 + -4) equal to 6.92820323 and -6.92820323.Subproblem 1
x2 + -4 = 6.92820323 Simplifying x2 + -4 = 6.92820323 Reorder the terms: -4 + x2 = 6.92820323 Solving -4 + x2 = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 6.92820323 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 6.92820323 + 4 x2 = 6.92820323 + 4 Combine like terms: 6.92820323 + 4 = 10.92820323 x2 = 10.92820323 Simplifying x2 = 10.92820323 Take the square root of each side: x = {-3.305783301, 3.305783301}Subproblem 2
x2 + -4 = -6.92820323 Simplifying x2 + -4 = -6.92820323 Reorder the terms: -4 + x2 = -6.92820323 Solving -4 + x2 = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -6.92820323 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -6.92820323 + 4 x2 = -6.92820323 + 4 Combine like terms: -6.92820323 + 4 = -2.92820323 x2 = -2.92820323 Simplifying x2 = -2.92820323 Reorder the terms: 2.92820323 + x2 = -2.92820323 + 2.92820323 Combine like terms: -2.92820323 + 2.92820323 = 0.00000000 2.92820323 + x2 = 0.00000000 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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