We'll just use F m a

So this fits the pattern of a perfect square.

These are halfpin barrel hinges.

This body uses hinge joints in the knees and elbows.

So if y 3, and z 2, then you're going to have the left hand expression is going to be x 3 2 which is going to be x 5

We don't want this 11 there.

Aligns formulas on the left side

My first rule is going to handle.

1 squared is 1.

And I have to square it.

So if we added a 9 here, we're actually adding 9 times 9 to the left hand side of the equation, so we have to add 81 to the right hand side to make the equation still hold.

Puts formula numbers on the left side

So let's factor out a 3x out of this expression on the left.

And then what do we get if we add 4 5 to both sides of this equation?

So this cannot equal 0.

Because you have this 4 multiplying it out front.

That gives us length squared, meters squared.

So plus b 2a squared.

So that the left hand side expression takes this form.

Now, just like the last problem, we want to turn this

It'll go from greater than to less than.

And in Chapter 11 restructuring, you keep operating the company.

Because you get it in this form and then you have to add this 64 here to kind of complete the square to turn this

If you press this button the equation on the left will be balanced.

And why did I add 64 to both sides of this equation?

Let's subtract it from the left hand side.

In fact, we know what a is. a is minus 7 12.

So I subtracted 20 from the left, let me also subtract 20 from the right.

Add a 1.

We have nothing out here, so we really just added a 1 to the

And we have 9x squared minus 42x, plus 29 is equal to negative 20.

Thrun And the answer is 3200cm or 32 meters.

If I take this and put it on this side of the equation, what happens?

... Right, left. Left, left, left, right, left.

Equation expressed through cosmological parameters.

What we do to one side, we have to do the other side.

So when you complete the square you want the thing to just look like a you want whatever's on the left hand side to look like a perfect square.

left hand side.

So let's divide by negative 13.

The answer is 200 mm for our focal length.

And so you get negative y plus 4 is equal to x.

Again, this is just basic algebra, whatever we do to one side we have to do to the other.

What you need to do here is put the entire quadratic expression on one side of the equation.

And, of course, this is the same thing as this.

linear equations. and you might be saying well you know, this is an equation,