00:01
Let's solve for x in this equation.
00:02
To begin, we want to eliminate some square roots.
00:05
So just as things are, i'm just going to square both sides.
00:09
Now, this is still going to leave us with some roots, but it's impossible to eliminate all the roots at the beginning.
00:14
So on the left, we're going to have x plus 7, that is this term squared, then plus 3 times the root plus 3 times the root, or plus 6 times the root, x plus 7, then plus 3 squared, or 9.
00:27
They'll be equal to this squared, which is just x minus 4.
00:32
So before we do anything else, we want to eliminate this root, meaning we'll have to get it alone on the left side.
00:39
So we can cancel an x from both sides, and then we can combine our like terms of 7 and 9.
00:46
This leaves us with 16 plus 6 square root 7 plus 9, or x plus 7, rather, equals negative 4.
00:56
If we subtract this 16 from both sides, we're going to end up with 6 square root x plus 7 equals, well, negative 4 minus 16 is going to be negative 20.
01:10
And now we can square both sides.
01:13
Leaving us with 36 times x plus 7 is equal to negative 20 squared or positive 400.
01:22
All right.
01:24
So next up, we're going to distribute on the left.
01:27
That is, we're going to multiply this 36 by the x plus 7, giving us x plus 7 times 36 is 252...