If we take the positive square root.

You can always every perfect square has a positive or a negative root.

So x is equal to 2 is 4.

You could rename it with anything really, is equal to the square root of x minus 1.

We can solve the mystery simply by looking at the actual difference between these two values.

I'll skip the actual computation of square roots here because this is the subject of another class, but before we return to the actual square root, we want to make sure that the square root actually is a square root.

Square Root

Square root

For example you cannot do this.

So the square root is this big check looking thing.

Well we go up three and down three.

Plus or minus the square root of 4 9 is 2 3, right?

Now some places you will see i defined this way

Square Root Scale

And then you get y is equal to and I'm doing this on purpose the plus or minus square root, because it can be the plus or minus square root.

Add them together, and then take the square root, or the principal root.

And I'm just going to re write it as y to the 1 2 power.

So let's see where that gets me.

And the same idea actually, can be done with any function.

So 4x plus 1 I'm just taking the square root of both sides.

Of x minus 1.

When we're taking the square root, it's not just the positive square root.

1,369 over 16.

So we're going to take the positive square root, or just the principal root, which is just the square root sign, of both sides.

Insert square root

5 minus 1 is 4.

Because then you could say, oh well the square root of negative nine is the same thing as i times the square root of nine, which equals threei.

Which tells us that the focal length is equal to the square root of this.

1,344 plus 25.

OK, so it's minus 5 plus or minus 37.

So we're shifting it over to the right by 5.

The square root of x.

So this point is equivalent to that point.

Instead of 8, let me write 8 as 4 times 2.

Now we can subtract 2 from both sides.

If we put an a here, we take f inverse of a.

When you just see a number under a radical sign like this, this means the principal square root of 9.

Is equal to the determinant of your matrix squared.

And this is just multiplying a binomial.

And then if we go to 2, let's see, 2 minus 1 is 1.

So this is 2 x 2 x 2 x 2, which is 16.

And our goal is to get back to negative 3.

So what are the solutions? t is equal to negatives b.

And we know if you take the absolute value of something, this is just a distance. It's going to be positive. So we want to take the positive square root, the principal square root, of both sides of this.

So the problem's this f of g of x hope I get this right