00:01
So we're going to look at solving this radical equation or square root equation.
00:04
The first thing we need to do is we need to isolate one of our square root terms.
00:09
So here we have one square root of x, here we have our other square root of x minus 5.
00:14
We're going to go ahead and isolate one of those and that way we can move on to our next step which would be squaring both sides.
00:22
So to isolate one of these terms we can do a couple different things.
00:27
First thing i'm going to do is just subtract x from both sides.
00:31
Now this gets me negative x minus 5 equals negative the square root of x plus 1.
00:40
And we can go ahead and further isolate this by dividing both sides by negative 1.
00:45
So we end up with the square root of x minus 5 equals square root of x minus 1.
00:53
Now that we have this isolated we can go ahead and move on to our next step which is squaring both sides.
01:01
So when we square the left hand side we're going to end up with x minus 5.
01:06
And when we square the right hand side we're going to end up with the square root of x minus 1 times the square root of x minus 1.
01:13
And this is where things get a little tricky because we're going to have to do some distribution.
01:19
Alright, things are getting a little bit messy so clean things up, move this up to the top and that will give us plenty of space to do our distribution.
01:26
So we're going to start out by doing the square root of x times the square root of x which is x.
01:31
Then we're going to do the square root of x times negative 1 which is negative 1 square root of x or just negative square root of x.
01:38
Then we're going to do the same thing here.
01:39
I'm writing that 1 because it will make things easier later on.
01:42
And we'll do negative 1 times negative 1 which is positive 1.
01:46
All that equals x minus 5.
01:50
Now we can do a little bit of combining of like terms here.
01:52
So we can have x minus 5 equals x minus 2 square root of x plus 1...