WEBVTT

1
00:00:00.000 --> 00:00:05.758
Here is the problem: x squared minus 13x plus 36 equals 0.

2
00:00:06.208 --> 00:00:10.260
A quadratic equation in x: solve with the quadratic formula.

3
00:00:11.060 --> 00:00:12.535
Start with the equation.

4
00:00:12.984 --> 00:00:15.979
Move every term to one side to get standard form.

5
00:00:16.429 --> 00:00:17.857
Compute the discriminant.

6
00:00:18.307 --> 00:00:22.382
delta greater than 0, so there are two distinct real roots.

7
00:00:23.182 --> 00:00:24.947
Apply the quadratic formula.

8
00:00:25.397 --> 00:00:27.022
Simplify each root.

9
00:00:27.472 --> 00:00:28.540
Factored form.

10
00:00:29.340 --> 00:00:33.276
Now look at the graph of the left side minus the right side.

11
00:00:33.726 --> 00:00:37.290
It crosses zero exactly at the solutions we found.

12
00:00:38.090 --> 00:00:41.910
So the answer is x equals 4 or x equals 9.

13
00:00:42.360 --> 00:00:48.571
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

14
00:00:49.371 --> 00:00:56.360
x equals 4: left side equals 0, right side equals 0, which checks out.

15
00:00:56.810 --> 00:01:03.381
x equals 9: left side equals 0, right side equals 0, which checks out.