# I need an algebra refresher

**URL:** <https://boards.straightdope.com/t/i-need-an-algebra-refresher/164047>\
**Category:** Factual Questions\
**Created:** [March 25, 2003, 4:29pm UTC](https://boards.straightdope.com/t/i-need-an-algebra-refresher/164047 "2003-03-25T16:29:02Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Hauky](https://avatars.discourse-cdn.com/v4/letter/h/0ea827/32.png) [@Hauky](https://boards.straightdope.com/u/Hauky)\
**Post date:** [March 25, 2003, 4:29pm UTC](https://boards.straightdope.com/t/i-need-an-algebra-refresher/164047/1 "2003-03-25T16:29:02Z")

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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?

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**Author:** ![Surreal](https://avatars.discourse-cdn.com/v4/letter/s/eada6e/32.png) [@Surreal](https://boards.straightdope.com/u/Surreal)\
**Post date:** [March 25, 2003, 4:34pm UTC](https://boards.straightdope.com/t/i-need-an-algebra-refresher/164047/2 "2003-03-25T16:34:44Z")

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Factor it out first.

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

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

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**Author:** ![Nametag](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nametag/32/406_2.png) [@Nametag](https://boards.straightdope.com/u/Nametag)\
**Post date:** [March 25, 2003, 4:39pm UTC](https://boards.straightdope.com/t/i-need-an-algebra-refresher/164047/3 "2003-03-25T16:39:35Z")

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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.

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**Author:** ![Hauky](https://avatars.discourse-cdn.com/v4/letter/h/0ea827/32.png) [@Hauky](https://boards.straightdope.com/u/Hauky)\
**Post date:** [March 25, 2003, 4:44pm UTC](https://boards.straightdope.com/t/i-need-an-algebra-refresher/164047/4 "2003-03-25T16:44:47Z")

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You’re all the coolest people ever. 😃

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**Author:** ![LordVor](https://avatars.discourse-cdn.com/v4/letter/l/90ced4/32.png) [@LordVor](https://boards.straightdope.com/u/LordVor)\
**Post date:** [March 25, 2003, 5:30pm UTC](https://boards.straightdope.com/t/i-need-an-algebra-refresher/164047/5 "2003-03-25T17:30:34Z")

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

-lv