00:01
Let's solve for x in this equation.
00:02
To begin, we want to get our x into a nicer form.
00:05
That is, these negative powers aren't very easy to solve with.
00:08
But if we create a new variable called u and set that equal to 1 over x or x the negative first power, things will be much easier to solve because we now have 7 u squared minus 10 u minus 8 equals 0, a much more solvable equation.
00:26
So this is a quadratic and it's somewhat difficult to factor, but it can still be done.
00:31
That is, we're going to have a 7x and an x, and then there's going to be a plus and a minus, since we know we're going to be multiplying to a negative number.
00:42
So what are our other numbers going to be? well, it's a bit complicated, but we need factors of eight.
00:47
So we can use 4 and 2, like so.
00:52
This will give us 7 times negative 2 is negative 14, then plus 4...