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Simplifying x4 + -8x2 + -64 = 0 Reorder the terms: -64 + -8x2 + x4 = 0 Solving -64 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -8x2 + 64 + x4 = 0 + 64 Reorder the terms: -64 + 64 + -8x2 + x4 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -8x2 + x4 = 0 + 64 -8x2 + x4 = 0 + 64 Combine like terms: 0 + 64 = 64 -8x2 + x4 = 64 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 = 64 + 16 Reorder the terms: 16 + -8x2 + x4 = 64 + 16 Combine like terms: 64 + 16 = 80 16 + -8x2 + x4 = 80 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x2 + -4) equal to 8.94427191 and -8.94427191.Subproblem 1
x2 + -4 = 8.94427191 Simplifying x2 + -4 = 8.94427191 Reorder the terms: -4 + x2 = 8.94427191 Solving -4 + x2 = 8.94427191 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 = 8.94427191 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 8.94427191 + 4 x2 = 8.94427191 + 4 Combine like terms: 8.94427191 + 4 = 12.94427191 x2 = 12.94427191 Simplifying x2 = 12.94427191 Take the square root of each side: x = {-3.59781488, 3.59781488}Subproblem 2
x2 + -4 = -8.94427191 Simplifying x2 + -4 = -8.94427191 Reorder the terms: -4 + x2 = -8.94427191 Solving -4 + x2 = -8.94427191 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 = -8.94427191 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -8.94427191 + 4 x2 = -8.94427191 + 4 Combine like terms: -8.94427191 + 4 = -4.94427191 x2 = -4.94427191 Simplifying x2 = -4.94427191 Reorder the terms: 4.94427191 + x2 = -4.94427191 + 4.94427191 Combine like terms: -4.94427191 + 4.94427191 = 0.00000000 4.94427191 + 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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