WEBVTT

1
00:00:00.000 --> 00:00:04.981
Here is the problem: 3x squared plus 18x equals 0.

2
00:00:05.431 --> 00:00:09.495
A quadratic equation in x: solve with the quadratic formula.

3
00:00:10.295 --> 00:00:11.746
Start with the equation.

4
00:00:12.196 --> 00:00:15.180
Move every term to one side to get standard form.

5
00:00:15.630 --> 00:00:17.000
Compute the discriminant.

6
00:00:17.450 --> 00:00:21.572
delta greater than 0, so there are two distinct real roots.

7
00:00:22.371 --> 00:00:24.089
Apply the quadratic formula.

8
00:00:24.539 --> 00:00:26.176
Simplify each root.

9
00:00:26.626 --> 00:00:27.682
Factored form.

10
00:00:28.483 --> 00:00:32.036
Now look at the graph of the left side minus the right side.

11
00:00:32.486 --> 00:00:36.236
It crosses zero exactly at the solutions we found.

12
00:00:37.036 --> 00:00:41.111
So the answer is x equals negative 6 or x equals 0.

13
00:00:41.561 --> 00:00:47.726
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

14
00:00:48.526 --> 00:00:55.922
x equals negative 6: left side equals 0, right side equals 0, which checks out.

15
00:00:56.372 --> 00:01:03.013
x equals 0: left side equals 0, right side equals 0, which checks out.