# How do you solve #x+5=sqrt(17+x)?#?

##### 2 Answers

#### Answer:

#### Explanation:

Square both sides

Subtract to make one side 0

Factor

Solve for x:

Since we squared both sides, we must check for extraneous solutions:

By convention, the

Therefore,

#### Answer:

#### Explanation:

First, square both sides:

We know that any binomial in the form of:

Put that back into the equation:

Subtract

This is in standard form, or **two numbers** that:

- Multiply up to
#color(red)(a)* color(magenta)(c) = color(red)(1) * color(magenta)(8) = 8# - Add up to
#color(green)(b)# , or#color(green)9#

Those two numbers are

#1 * 8 = 8# #1 + 8 = 9#

Therefore, the factored form is:

Since when the expressions multiply to equal zero, that means each of the expressions equal zero. So we can set up two equations:

Subtract

Now we have to check if both solutions are really solutions by plugging them into the original formula. Let's check

No, this is not true, so **NOT** a solution! Now check

Yes, this is true, so **ONLY** solution!

Hope this helps!