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Simplifying x4 + 8x2 + -12 = 0 Reorder the terms: -12 + 8x2 + x4 = 0 Solving -12 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 8x2 + 12 + x4 = 0 + 12 Reorder the terms: -12 + 12 + 8x2 + x4 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 8x2 + x4 = 0 + 12 8x2 + x4 = 0 + 12 Combine like terms: 0 + 12 = 12 8x2 + x4 = 12 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 = 12 + 16 Reorder the terms: 16 + 8x2 + x4 = 12 + 16 Combine like terms: 12 + 16 = 28 16 + 8x2 + x4 = 28 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x2 + 4) equal to 5.291502622 and -5.291502622.Subproblem 1
x2 + 4 = 5.291502622 Simplifying x2 + 4 = 5.291502622 Reorder the terms: 4 + x2 = 5.291502622 Solving 4 + x2 = 5.291502622 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 = 5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 5.291502622 + -4 x2 = 5.291502622 + -4 Combine like terms: 5.291502622 + -4 = 1.291502622 x2 = 1.291502622 Simplifying x2 = 1.291502622 Take the square root of each side: x = {-1.136442969, 1.136442969}Subproblem 2
x2 + 4 = -5.291502622 Simplifying x2 + 4 = -5.291502622 Reorder the terms: 4 + x2 = -5.291502622 Solving 4 + x2 = -5.291502622 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 = -5.291502622 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -5.291502622 + -4 x2 = -5.291502622 + -4 Combine like terms: -5.291502622 + -4 = -9.291502622 x2 = -9.291502622 Simplifying x2 = -9.291502622 Reorder the terms: 9.291502622 + x2 = -9.291502622 + 9.291502622 Combine like terms: -9.291502622 + 9.291502622 = 0.000000000 9.291502622 + 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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