Question

College Algebra: I'm reviewing for my Final coming up and I need tons of help. Some of the math problems I'm going through are not making sense. The math problem will be in the comments:

Answer 1

\[\sqrt{x+10}=x-2\]

Answer 2

You have the square root isolated on the left side. What you can do is square both sides to undo the square root (which effectively gets rid of the square root).

Answer 3

What do you get when you do this?

Answer 4

Wouldn't you try to get x alone on one side?

Answer 5

Yes that is the ultimate goal, but first you need to get rid of the square root.

Answer 6

I thought we got rid of the square root

Answer 7

Well you have \(\sqrt{x+10}=x-2\) right?

Answer 8

I see the square root on the left side.

Answer 9

Yes. You said we square root both sides, so wouldn't it be:
\[\sqrt{x+10}=\sqrt{x-2}\]

Answer 10

Square, not square root

Answer 11

oops lolx

Answer 12

Try it again.

Answer 13

So it's more like
\[(x+10=x-2)^{2}\]
or
\[x+10=(x-2)^{2}\]

Answer 14

The notation would look like this:
\[\Large \sqrt{x+10}=x-2\]
\[\Large (\sqrt{x+10})^2=(x-2)^2\]
\[\Large x+10=(x-2)^2\]
Notice how squaring the \(\sqrt{x+10}\) makes it turn into \(x+10\)

Answer 15

So, I was right; yay! :)

Answer 16

yes be sure to apply the square to both sides where each side gets their own square exponent

Answer 17

Okay, so the equation would be x+10=x^2 +4?

Answer 18

no

Answer 19

\((x-2)^2\) is NOT equal to \(x^2+4\) (common mistake)

Answer 20

Oh?

Answer 21

You have to use the FOIL rule.

Answer 22

\((x-2)^2 = (x-2)(x-2) = ??\)

Answer 23

Oh I got it.
\[x ^{2}-4x+4\]

Answer 24

better

Answer 25

You now should have

\[\Large x+10 = x^2-4x+4\]

Answer 26

Okay, i do

Answer 27

Do you see how to solve from here?

Answer 28

I'm thinking of moving what's on the left to the right

Answer 29

That will work.

Answer 30

Alright, I got \[x ^{2}-5x-6\]

Answer 31

good

Answer 32

that's equal to 0

Answer 33

Oops, I mean
\[x ^{2}-5x-6=0\]

Answer 34

That's ok, I knew what you meant.

Answer 35

Okay good :D

Answer 36

So, that's the answer?

Answer 37

No, you need to isolate x. You can factor, complete the square or use the quadratic formula.

Answer 38

I'll use the quadratic formula

Answer 39

That's a good idea since the quadratic formula works for any quadratic equation.

Answer 40

Yeah, plus it's my favorite formula :D

Answer 41

Alright, as far as I got. It's
\[x=\frac{ 5\pm7 }{ 2 }\]

Answer 42

very good

Answer 43

so what are the two possible solutions?

Answer 44

\[x=\frac{ 5+7 }{ 2 }\] and \[x=\frac{ 5-7 }{ 2 }\]

Answer 45

wait a minute...

Answer 46

you can keep going to simplify

Answer 47

Yeah, that's what I was thinking. So the two solutions are 6 and -1

Answer 48

They are the possible solutions, so you'll need to check them both in the original equation.

Answer 49

Only 6 works because -1 makes the equation false

Answer 50

Very good.

Answer 51

Yes!!!! Thank you so much!! :) I truly do appreciate it :)

Answer 52

you're welcome