# How do you solve #sqrt(3x+10)=sqrt(x+11)-1#?

##### 1 Answer

#### Answer:

#### Explanation:

Square both sides:

The square of a square root is simply what's on the inside. So the left side is simply:

However, the right side, you have to distribute. Use FOIL:

Again, the square root cancels with the squared:

Combine like terms:

Now write both sides together:

Isolate the square root by subtracting

Let's simplify the left side:

Now we have another square root so we have to square both sides again:

The square root cancels with the square:

Distribute on the left side:

Simplify the left side:

Move everything to the left by subtracing

Factor:

Set

Plug back in to check:

This doesn't work so 5 is an extraneous variable. Now the other one:

That works! So we only have