solve the equation after making an appropriate substitution x^4-22x^2+96=0

This equation factors.

x^{4} - 22x^{2 }+ 96=0

(x^{2 }- 16)(x^{2} - 6) = 0

x^{2} = 16 or 6

x = ±4 or ±√6

solve the equation after making an appropriate substitution x^4-22x^2+96=0

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This equation factors.

x^{4} - 22x^{2 }+ 96=0

(x^{2 }- 16)(x^{2} - 6) = 0

x^{2} = 16 or 6

x = ±4 or ±√6

You could make a substitution **u = x ^{2}**

You can rewrite **x ^{4} - 22x^{2} + 96 = 0** as

**(x ^{2})^{2} - 22(x^{2}) + 96 = 0** which makes it easier to see where to make the substitution:

**u ^{2} - 22u + 96 = 0**

now factor it by finding two numbers which multiply to equal 96, and add up to -22: (-6)*(-16) = 96 and (-6) + (-16) = -22

**(u - 16)(u - 6) = 0**

u = 16 or u = 6. Remember that u = x^{2} and now you can solve it as Roman did.