I need an algebra refresher

x^4 + 9(x^2) = 70. Solve for x.

Now, I know this can be solved, because my calculator does it (+ or - square root of 5). I just can’t figure out how it does it! All I’m seeing is two different terms (x^4 and x^2) in a single equation. I’m fairly sure it’s got to involve dividing the first term by the second, leaving you with just x^2, but I can’t get that to happen without ending up with 70/x^2 or some such nonsense. Help?

Factor it out first.

x^4 + 9*x^2 - 70 = 0 goes to

(x^2 + 14) ( x^2 - 5) = 0

Substitute y for x[sup]2[/sup]. Now you have a quadratic equation. Find the roots and go back to y = x[sup]2[/sup] to solve for x.

You’re all the coolest people ever. :smiley:

Note that + or - the square root of (-14) is also a valid, if imaginary, answer.