# How do you solve #\sqrt{x}=x-6#?

##### 3 Answers

#### Explanation:

Square the equation:

Apply the expansion of

Factorize the quadratic.

Note that substituting 4 in the equation returns 2 = -2, which is obviously wrong. So we neglect x = 4 in the set of solutions. Take care to verify your answers after solving(don't make my mistake!)

#### Explanation:

First, square both sides:

Simplify:

Move everything to one side of the equation:

Now we need to factor.

Our equation is standard form, or

The factored form is

We have two rules to find

#m# and#n# have to**multiply**up to#a * c# , or#36# #m# and#n# have to**add**up to#b# , or#-13#

Those two numbers are

Therefore,

However, we still need to **check our answers** by substituting them back into the original equation, since we have a square root in our original equation.

Let's first check if

This is not true! That means that

Now let's check

This is true! That means that

So the final answer is

Hope this helps!

#### Explanation:

First, square both sides of this equation.

Now put in standard form.

Factor.

When we squared both sides to at the beginning, we enabled an extraneous solution since