So what does this simplify to?

And all of these are divisible by 5.

So let's multiply both sides by mu.

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.

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.

Times v1 dot v1.

And this number is the same as this number.

We have all of that over minus 16.

So this whole expression simplifies to

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

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.

Times negative one.

What's that going to simplify to?

Minus va minus 400 12.

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.

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.

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

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.

This is where we just get our algebra hat on, and try to simplify until it's a separable equation in v.

No, my brougham is waiting.

Remember, this thing is just this thing right here, we're just doing the Pythagorean theorem.

It's just making sure we're multiplying every part of this number, times every part of that number.

6 plus 2 is 8.

Marketing people have never been able to do that.

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

So it's very valuable to have this mathematical, rigorous, thinking.