x^4+4x^2+21=0

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Solution for x^4+4x^2+21=0 equation:


Simplifying
x4 + 4x2 + 21 = 0

Reorder the terms:
21 + 4x2 + x4 = 0

Solving
21 + 4x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 4x2 + -21 + x4 = 0 + -21

Reorder the terms:
21 + -21 + 4x2 + x4 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 4x2 + x4 = 0 + -21
4x2 + x4 = 0 + -21

Combine like terms: 0 + -21 = -21
4x2 + x4 = -21

The x term is 4x2.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x2 + 4 + x4 = -21 + 4

Reorder the terms:
4 + 4x2 + x4 = -21 + 4

Combine like terms: -21 + 4 = -17
4 + 4x2 + x4 = -17

Factor a perfect square on the left side:
(x2 + 2)(x2 + 2) = -17

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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