Can someone check my work for me?

Question

here is the problem:

x=(sqrtx+13)+7

i have the answer as 3, 12

Answer 1

Isolate the numbers under the √ symbol

x-7= √x+13

Square both sides of the equation. On the right side, it's as simple as removing the √ symbol. On the left side, however, you need to use FOIL.

x^2-14x+49=x+13

Move everything to one side.

x^2-15x+36=0

Factor.

(x-3 )(x-12 )=0

Solve each term.

x-3=0

x=3

x-12=0

x=12

Check.

12=√(25)+7=5+7=12

3=√16+7=/=4+7

The answer is 12.

Answer 2

x = 12 is correct but NOT x = 3.

All you have to do is check them back in the original equation.

12 =? sqrt(12 + 13) + 7 = 5 + 7 OK

3 =? sqrt(3 + 13) + 7 NO.

I know that the working led you to these two answers, but you will find that squaring often introduces false solutions. You should always check answers back in original equations.