Solving radical equations
square root x+7 = x - 5

So the square root of the quatity(x+7)=x-5

so you square both sides and get rid of the square root
x+7=(x-5)^2
(x-5)^2=x^2-10x+25
x+7=x^2-10x+25
subtract 7 from both sides
x=x^2-10x+18
subtract x from both sides
0=x^2-11x+18

so if xy=0 we can assume that x or/and y =0

factor out x^2-11+18
(find what two numbers multiply to get 18 and add to get -11)
-2 times -9=18
-2+(-9)=-11

(x-2)(x-9)=0
set them to zero
x-2=0
x=2

x-9=0
x=9

there are two answers -2 and -9

The domain:
The radicand must be greater than or equal to 0.

The value of the square root must be greater than or equal to 0.

Therefore x≥5.


2<5 so it's not a correct solution.
9≥5 so it's a correct solution.

The
x=9