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Simplifying x4 + 8x2 + 1 = 0 Reorder the terms: 1 + 8x2 + x4 = 0 Solving 1 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 8x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 8x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8x2 + x4 = 0 + -1 8x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 8x2 + x4 = -1 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 = -1 + 16 Reorder the terms: 16 + 8x2 + x4 = -1 + 16 Combine like terms: -1 + 16 = 15 16 + 8x2 + x4 = 15 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x2 + 4) equal to 3.872983346 and -3.872983346.Subproblem 1
x2 + 4 = 3.872983346 Simplifying x2 + 4 = 3.872983346 Reorder the terms: 4 + x2 = 3.872983346 Solving 4 + x2 = 3.872983346 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 = 3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 3.872983346 + -4 x2 = 3.872983346 + -4 Combine like terms: 3.872983346 + -4 = -0.127016654 x2 = -0.127016654 Simplifying x2 = -0.127016654 Reorder the terms: 0.127016654 + x2 = -0.127016654 + 0.127016654 Combine like terms: -0.127016654 + 0.127016654 = 0.000000000 0.127016654 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 4 = -3.872983346 Simplifying x2 + 4 = -3.872983346 Reorder the terms: 4 + x2 = -3.872983346 Solving 4 + x2 = -3.872983346 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 = -3.872983346 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -3.872983346 + -4 x2 = -3.872983346 + -4 Combine like terms: -3.872983346 + -4 = -7.872983346 x2 = -7.872983346 Simplifying x2 = -7.872983346 Reorder the terms: 7.872983346 + x2 = -7.872983346 + 7.872983346 Combine like terms: -7.872983346 + 7.872983346 = 0.000000000 7.872983346 + 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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