So what does this simplify to?

And all of these are divisible by 5.

So let's multiply both sides by mu.

We have all of that over minus 16.

So this whole expression simplifies to

And that can also be written as and this is my preferred notation, because it doesn't have all this extra junk everywhere.

The trick here is to factor it and simplify it before you do any multiplication.

So 4 9 is the exact same thing as 16 36.

The length is given right over there it is a squared plus 6 a minus 27 they want us to simplify this.

Colour, Floyd Steinberg, CMYK, simpler

Color, Floyd Steinberg, CMYK, simpler

And then you make some assumptions about it.

I'm starting to see the light at the end of the tunnel.

let's cancel that out.

25i 2 is the same thing as 25 times 1, so that is 25.

You would get 8 minus 4 is 4.

What's that going to simplify to?

Because if we just simplify this expression, and we include things in the simplified domain that weren't included in the original function's domain, we've actually changed the expression.

Times v1 dot v1.

And this number is the same as this number.

Is given right up here, is 2x times the principal square root of 5 minus 4, minus 4.

So we start with 5x 2(7x 1) 14x

We have one expression on top of another expression.

let's cancel that out.

Well, a is minus 10, so 2 times a is minus 20.

We have a b squared over b to the third power

You could bring the 13 down here if you want to write it so you don't have a fraction over a fraction.

6 plus 2 is 8.

Times negative one.

Minus va minus 400 12.

Now, this is actually the hardest part with the quadratic equation is oftentimes just simplifying this expression.

I think we're almost there.

So this is going to be equal to, if we distribute onto that, we get. Minus 2x times the principle square root of 5. Negative 1 times negative 4, is plus or positive 5, and now we can simplify.

So the number of units we have in the output layer is going to be equal to one.

All we did is wherever we saw an x, we substituted it, minus 2 there.

But because this is an equation, it equals 0, let's just divide everything by 9.

We've stated the domain.

These will make this expression undefined. It will make this denominator equal to 0.

The numerator has the same degree as the denominator.

And let's see what this simplifies to.

So we can do this in multiple ways, simplify different parts.

So let's factor out a 6. And then 12x divided by 6 is 2x. And then 30 divided by 6 is 5.

So we can write this as x plus 2 times x plus 8.

And you could leave it this way, or you could actually try to simplify this a little bit.

That comes from algebra.