Here, if we let u = x2, we can rewrite the equation so it looks like an ordinary quadratic equation:

u2 − 20u + 64 = 0

We now factor to give:

(u − 16)(u − 4) = 0

So the solutions for u are 16 or 4.

So `x^2= 16` or `x^2= 4`.

These give us:

x = −4 or 4 x = −2 or 2

So the complete set of solutions is: `x = −4, −2, 2, 4`.

Is it correct?

The sketch shows:

123456-1-2-3-4-5-650100-50xyOpen image in a new page

`y = x^4 - 20x^2 + 64`, showing intersections with the x-axis

We can see from where the graph cuts the x-axis that the solutions are correct.

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