So, I'll see you in the part 2 of using the quadratic equation.

But anyway I don't want to get caught up in terminology.

You might have to use a quadratic equation or something.

And we are done.

I just subtracted 16 from both sides to get here.

And maybe I'll show you in a future video, the quadratic equation and I think I've already done one where I proved the quadratic equation.

Bx plus C is equal to 0.

And this is a good idea to memorize.

Now we have a quadratic expression equaling 0.

So let's say I have a quadratic equation.

All right, this is another one that should be cut and pasted. All right, four steps to derive the quadratic formula are shown below.

But with that said, any number times this imaginary unit i is an imaginary number.

For deflections further out you'll see only distortions but generally not multi split images, that's called the weak lensing regime.

So let's do that.

Oh this is a dog, got it? All right!

Welcome to the presentation on using the quadratic equation.

I'm actually out of space. OK, they want to know the solution set to this quadratic equation.

And that's even worse to factor just by inspection.

But how about in math? where we're like, Ok, hey, come here, quadratic formula!

So what x's are valid?

This is not a trivial one for me to factor so, if it's not trivial, you can just use the quadratic equation.

So the first thing we want to do here is not to factor this

What's completing the square?

look like, because these are all parabolas, or the graph of a quadratic equation.

See, normally in school, you do things like solve quadratic equations.

0.2 times x is equal to 4.

Right?

learned before, but it's a neat trick.

But anyway, these are useful properties to maybe internalize for second order homogeneous linear differential equations.

Problem 60.

Or likewise.

And then complete the square using the a, b, and c's instead of numbers.

This isn't something that you would factor.

And we've factored our binomial.

And then the right hand side will be equal to 0.

And this one is called homogeneous.

linear equations right here.

Or you should write it down on a piece of paper.

And then all you have left is Step ill.

So hopefully you found that helpful, this whole notion of completing the square.

So let's just start with a review of what the quadratic equation is.

So the first thing you want to start off with is just a quadratic equation.

You essentially complete the square with arbitrary numbers a, b, and c, and you get the quadratic equation.

Now here's a video game teaching that very same content.

I would say a lot easier than what we did in the previous first order homogeneous difference equations, or the exact equations.