Easy Solution for x + √x = 90: List of Solutions | Midterm Math Troubles

[MacLaddy]

Homework Statement

Okay, so I just got home a few moments ago from the first of two midterms that I will have to take this year, (do the math on that one) and I can not seem to figure out the very first problem that was listed on the test.

It was

x + $$\sqrt{x}$$ = 90

Homework Equations

It says "List all solutions"

The Attempt at a Solution

I tried several things, but none that seemed to fit correctly. Just by looking at it I can see that one of the solutions is x=81, but I can't get it to spit that out algebraically.

I've isolated the radical, then squared both sides to give myself a quadratic, but when I solve that I get two answers that do not work.

I'm sure this is an easy question, and one that I should know. It will probably wake me up in the middle of the night, but it's driving me crazy for now.

 

[MacLaddy]

Oh good grief... I got it.

I wasn't squaring 90-x together and foiling.

x = (90-x)^2

I was squaring them individually

x = 8100+x^2