WEBVTT

1
00:00:00.000 --> 00:00:05.143
Here is the problem: x squared plus 12x plus 27 equals 0.

2
00:00:05.593 --> 00:00:09.680
A quadratic equation in x: solve with the quadratic formula.

3
00:00:10.480 --> 00:00:12.001
Start with the equation.

4
00:00:12.451 --> 00:00:15.586
Move every term to one side to get standard form.

5
00:00:16.036 --> 00:00:17.441
Compute the discriminant.

6
00:00:17.891 --> 00:00:21.804
delta greater than 0, so there are two distinct real roots.

7
00:00:22.604 --> 00:00:24.311
Apply the quadratic formula.

8
00:00:24.761 --> 00:00:26.421
Simplify each root.

9
00:00:26.871 --> 00:00:27.893
Factored form.

10
00:00:28.693 --> 00:00:32.339
Now look at the graph of the left side minus the right side.

11
00:00:32.789 --> 00:00:36.458
It crosses zero exactly at the solutions we found.

12
00:00:37.258 --> 00:00:41.972
So the answer is x equals negative 9 or x equals negative 3.

13
00:00:42.422 --> 00:00:48.796
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

14
00:00:49.596 --> 00:00:57.061
x equals negative 9: left side equals 0, right side equals 0, which checks out.

15
00:00:57.511 --> 00:01:04.709
x equals negative 3: left side equals 0, right side equals 0, which checks out.