3x^4-10x^2+45=0

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Solution for 3x^4-10x^2+45=0 equation:


Simplifying
3x4 + -10x2 + 45 = 0

Reorder the terms:
45 + -10x2 + 3x4 = 0

Solving
45 + -10x2 + 3x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
15 + -3.333333333x2 + x4 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -3.333333333x2 + -15 + x4 = 0 + -15

Reorder the terms:
15 + -15 + -3.333333333x2 + x4 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -3.333333333x2 + x4 = 0 + -15
-3.333333333x2 + x4 = 0 + -15

Combine like terms: 0 + -15 = -15
-3.333333333x2 + x4 = -15

The x term is -3.333333333x2.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x2 + 2.777777779 + x4 = -15 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x2 + x4 = -15 + 2.777777779

Combine like terms: -15 + 2.777777779 = -12.222222221
2.777777779 + -3.333333333x2 + x4 = -12.222222221

Factor a perfect square on the left side:
(x2 + -1.666666667)(x2 + -1.666666667) = -12.222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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