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Simplifying x4 + -8x2 + -25 = 0 Reorder the terms: -25 + -8x2 + x4 = 0 Solving -25 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -8x2 + 25 + x4 = 0 + 25 Reorder the terms: -25 + 25 + -8x2 + x4 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -8x2 + x4 = 0 + 25 -8x2 + x4 = 0 + 25 Combine like terms: 0 + 25 = 25 -8x2 + x4 = 25 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 = 25 + 16 Reorder the terms: 16 + -8x2 + x4 = 25 + 16 Combine like terms: 25 + 16 = 41 16 + -8x2 + x4 = 41 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x2 + -4) equal to 6.403124237 and -6.403124237.Subproblem 1
x2 + -4 = 6.403124237 Simplifying x2 + -4 = 6.403124237 Reorder the terms: -4 + x2 = 6.403124237 Solving -4 + x2 = 6.403124237 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 = 6.403124237 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 6.403124237 + 4 x2 = 6.403124237 + 4 Combine like terms: 6.403124237 + 4 = 10.403124237 x2 = 10.403124237 Simplifying x2 = 10.403124237 Take the square root of each side: x = {-3.225387455, 3.225387455}Subproblem 2
x2 + -4 = -6.403124237 Simplifying x2 + -4 = -6.403124237 Reorder the terms: -4 + x2 = -6.403124237 Solving -4 + x2 = -6.403124237 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 = -6.403124237 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -6.403124237 + 4 x2 = -6.403124237 + 4 Combine like terms: -6.403124237 + 4 = -2.403124237 x2 = -2.403124237 Simplifying x2 = -2.403124237 Reorder the terms: 2.403124237 + x2 = -2.403124237 + 2.403124237 Combine like terms: -2.403124237 + 2.403124237 = 0.000000000 2.403124237 + 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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