x^4+2x^2+81=0

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Solution for x^4+2x^2+81=0 equation:


Simplifying
x4 + 2x2 + 81 = 0

Reorder the terms:
81 + 2x2 + x4 = 0

Solving
81 + 2x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-81' to each side of the equation.
81 + 2x2 + -81 + x4 = 0 + -81

Reorder the terms:
81 + -81 + 2x2 + x4 = 0 + -81

Combine like terms: 81 + -81 = 0
0 + 2x2 + x4 = 0 + -81
2x2 + x4 = 0 + -81

Combine like terms: 0 + -81 = -81
2x2 + x4 = -81

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = -81 + 1

Reorder the terms:
1 + 2x2 + x4 = -81 + 1

Combine like terms: -81 + 1 = -80
1 + 2x2 + x4 = -80

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -80

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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