Question

Can someone please help me? 5+(sqrt(x+2))=8+(sqrt(x-7))

Answer 1

solving for x I assume

Answer 2

I would isolate one of the sqrt( ) things then square both sides

Answer 3

\[\sqrt{x+2}=3+\sqrt{x-7}\]
square both sides
what do you get after doing just this step

Answer 4

Do I square both sides?

Answer 5

yes that is what I'm asking you to do :p

Answer 6

x+2=9+x-7?

Answer 7

well that isn't exactly how you square the right hand side

Answer 8

How would you do it then. That's the part I'm so confused on lol

Answer 9

\[(\sqrt{x+2})^2=(3+\sqrt{x-7})^2 \\ x+2=(3+\sqrt{x-7})(3+\sqrt{x-7})\]

Answer 10

Ok that would make sense..But then what..?

Answer 11

multiply

Answer 12

\[x+2=9+6(\sqrt{x-7})^2+x-7\]

Answer 13

Is that right?

Answer 14

well almost

Answer 15

the square there shouldn't be on that radical part

Answer 16

\[x+2=9+6 \sqrt{x-7}+x-7 \]

Answer 17

now we want to isolate the square root item
and then square both sides again

Answer 18

subtract x on both sides
+ 7 on both sides
- 9 on both sides

Answer 19

\[7-9+2=6 \sqrt{x-7}\]

Answer 20

combine like terms on left hand side

Answer 21

divide both sides by 6

Answer 22

and then square both sides

Answer 23

You are my hero xD Thank you so much!!!

Answer 24

make sure you check the answer by pluggin it into the original equation