Answer:
x = (±√7 ±i)/2
Step-by-step explanation:
The equation can be rewritten to look like a quadratic in x². In standard form, it is ...
(x²)² -3x² +4 = 0
Then by the quadratic formula, ...
x² = (-(-3) ± √((-3)²-4(1)(4)))/(2(1)) = (3 ± √-7)/2
x = ±√((3 ±i√7)/2)
This can be simplified to ...
x = ±(√7)/2 ±i/2
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Comment on simplification
The method I used was a combination of numerical technique and guessing. The value of x has a rational imaginary part, so we guessed that the real part was a simple square root. That guess turned out to be accurate.
