x^4+6x^2+42=0

Solution for x^4+6x^2+42=0 equation:

Simplifying
x4 + 6x2 + 42 = 0

Reorder the terms:
42 + 6x2 + x4 = 0

Solving
42 + 6x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + 6x2 + -42 + x4 = 0 + -42

Reorder the terms:
42 + -42 + 6x2 + x4 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 6x2 + x4 = 0 + -42
6x2 + x4 = 0 + -42

Combine like terms: 0 + -42 = -42
6x2 + x4 = -42

The x term is 6x2.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x2 + 9 + x4 = -42 + 9

Reorder the terms:
9 + 6x2 + x4 = -42 + 9

Combine like terms: -42 + 9 = -33
9 + 6x2 + x4 = -33

Factor a perfect square on the left side:
(x2 + 3)(x2 + 3) = -33

Can't calculate square root of the right side.

The solution to this equation could not be determined.