ShmoopTube

00:03

Solving Quadratic Equations: The Quadratic Formula, a la Shmoop.

00:09

Since the Dark Ages, the alchemists of Eureka, Incorporated have been trying as hard as they [Alchemist of Eureka beside a spinning blue ball]

00:14

can to turn lead into gold.

00:16

They've experimented with every formula known to man: the Empirical formula, the Hardy-Weinberg [Alchemist throws an ornament into a cauldron]

00:22

formula, Formula 409.

00:25

Now they will try...

00:27

…The Quadratic Formula.

00:29

First, they have to uncover this ancient formula, which hasn't been seen by man in thousands [Roll of parchment unfurls to show the quadratic formula]

00:33

of years....

00:35

Wait, what's that?

00:36

It's taught in pretty much every high school math class? [Alchemist looking bemused in a class teaching students about quadratic formula]

00:39

This formula reads: x equals negative b plus-or-minus the square root of b-squared

00:46

minus four-a-c over two-a.

00:51

In order to work their magic, the alchemists have to solve for x in this equation: [quadratic equation filled in to solve for x]

00:55

Three-x-squared equals two-x plus five...

00:59

First, they need to change the equation into this form: [equation switched into a new form]

01:03

a-x squared plus b-x plus c equals zero.

01:09

Looks like they're going to subtract two-x and five from both sides, leaving us with...

01:14

…three-x-squared minus two-x minus five equals zero.

01:18

Now it's time to apply the formula. [girl applying make-up on another girls face]

01:21

X equals two plus-or-minus the square root of negative two squared, minus four times

01:27

three times negative five, all this over two times three.

01:32

This simplifies to two plus or minus the square-root of four plus sixty, over six.

01:38

Furthermore, this simplifies to two plus or minus the square-root of sixty-four over six.[quadratic equation formula simplified]

01:46

The square-root of sixty-four is eight, and since our equation is plus or minus… [tree roots sprinkled with a magic wand]

01:50

We have two equations now,

01:53

x equals two plus eight over six

01:56

and x equals two minus eight over six.

02:00

Two plus eight equals ten, so x equals ten over six, which reduces to five over three.

02:07

As for the other one, two minus eight equals negative six.

02:11

Negative six over six reduces to negative one.

02:15

X equals negative one.

02:16

And... that's about it.

02:18

They didn't turn lead into gold, but they turned one math problem into two solutions. [Alchemist tosses math formula into a cauldron]

02:22

That's something, right?

02:23

Still, it's better than that time they tried baby formula. [baby formula thrown into the blue cauldron]

02:26

They ended up with more babies than they knew what to do with. [babies appear out of the blue cauldron]

Full Transcript