Question

solve. check for extraneous solutions.
sqrt x+56=x
4
-4
8
-8

Answer 1

\(\sqrt{x} + 56 = x\)

Move the 56 to the right side by subtracting it from both sides.
Then square both sides to get rid of the square root.
What do you get?

Answer 2

x^2-x-56=0
x^2+(a+b)x+ab=(x+a)(x+b)
(x-8)(x+7)=0
x-8=0
x=8
x+7=0
x=-7
x=8,-7

Answer 3

@E.ali
You solved your equation correctly, but that equation is not equivalent to the equation in the original post.

To find the equivalent equation without a square root, follow my suggestion above.
Then make sure you check the solutions in the original equation since squaring both sides of an equation may introduce extraneous solutions.