# Solving Quadratic Equations Using the Quadratic Formula

To solve using the quadratic equation, you need to find your a, b, and c values. Once you have that, just plug them into the formula, simplify, and solve. Easy as... the quadratic equation!

Language | English Language |

Quadratic Equations | Quadratic Equations |

### Transcript

Now they will try...

…The Quadratic Formula.

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]

of years....

Wait, what's that?

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

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

minus four-a-c over two-a.

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

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

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

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

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

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

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

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

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

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

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

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

We have two equations now,

x equals two plus eight over six

and x equals two minus eight over six.

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

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

Negative six over six reduces to negative one.

X equals negative one.

And... that's about it.

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

That's something, right?

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

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