# How do you solve #x= sqrt(6x) +7#?

##### 2 Answers

#### Explanation:

First let's define the domain :

So:

So :

\0/ herex's our answer!

Bare with me please: this is a long solution process:

#### Explanation:

We can subtract

We can square both sides to get:

What I have in blue, we can use the highly useful mnemonic **FOIL** to simplify this. We simply multiply the first terms, outside terms, inside and last terms. We get:

- First terms:
#x*x=x^2# - Outside terms:
#x*-7=-7x# - Inside terms:
#-7*x=-7x# - Last terms:
#-7*-7=49#

Now, we have:

Which can be simplified to

We have a quadratic on the left, so we want to set it equal to zero to find its zeroes. We do this by subtracting

The only factors of **quadratic formula**:

where

Plugging into the quadratic formula, we get:

Which simplifies to

Because

Which obviously simplifies to

Now, we have

Every term is divisible by

Which is equal to

Since our answer had a square root in it, we know the **domain has to be #x>=0#**.

as our **final** solution.

This was a long solution process, but all I did was:

- Get
#x# on one side - Square both sides to get rid of the square root
- Used
**FOIL**to simplify the left side - Used the
**Quadratic Formula** - Checked the domain

I really hope this helps!