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Simplifying x4 + 8x2 + -24 = 0 Reorder the terms: -24 + 8x2 + x4 = 0 Solving -24 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 8x2 + 24 + x4 = 0 + 24 Reorder the terms: -24 + 24 + 8x2 + x4 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 8x2 + x4 = 0 + 24 8x2 + x4 = 0 + 24 Combine like terms: 0 + 24 = 24 8x2 + x4 = 24 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 = 24 + 16 Reorder the terms: 16 + 8x2 + x4 = 24 + 16 Combine like terms: 24 + 16 = 40 16 + 8x2 + x4 = 40 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x2 + 4) equal to 6.32455532 and -6.32455532.Subproblem 1
x2 + 4 = 6.32455532 Simplifying x2 + 4 = 6.32455532 Reorder the terms: 4 + x2 = 6.32455532 Solving 4 + x2 = 6.32455532 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 = 6.32455532 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 6.32455532 + -4 x2 = 6.32455532 + -4 Combine like terms: 6.32455532 + -4 = 2.32455532 x2 = 2.32455532 Simplifying x2 = 2.32455532 Take the square root of each side: x = {-1.524649245, 1.524649245}Subproblem 2
x2 + 4 = -6.32455532 Simplifying x2 + 4 = -6.32455532 Reorder the terms: 4 + x2 = -6.32455532 Solving 4 + x2 = -6.32455532 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 = -6.32455532 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -6.32455532 + -4 x2 = -6.32455532 + -4 Combine like terms: -6.32455532 + -4 = -10.32455532 x2 = -10.32455532 Simplifying x2 = -10.32455532 Reorder the terms: 10.32455532 + x2 = -10.32455532 + 10.32455532 Combine like terms: -10.32455532 + 10.32455532 = 0.00000000 10.32455532 + 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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