WEBVTT

1
00:00:00.000 --> 00:00:04.226
Here is the problem: 6/x equals x minus 1.

2
00:00:04.676 --> 00:00:08.821
A quadratic equation in x: solve with the quadratic formula.

3
00:00:09.621 --> 00:00:11.072
Start with the equation.

4
00:00:11.522 --> 00:00:21.855
Multiply both sides by x to clear the fractions. This is only valid where x not equal to 0, so any value that makes it zero is excluded at the end.

5
00:00:22.305 --> 00:00:25.335
Move every term to one side to get standard form.

6
00:00:25.785 --> 00:00:27.178
Compute the discriminant.

7
00:00:27.978 --> 00:00:32.111
delta greater than 0, so there are two distinct real roots.

8
00:00:32.561 --> 00:00:34.268
Apply the quadratic formula.

9
00:00:34.718 --> 00:00:36.285
Simplify each root.

10
00:00:36.735 --> 00:00:37.803
Factored form.

11
00:00:38.603 --> 00:00:42.144
Now look at the graph of the left side minus the right side.

12
00:00:42.594 --> 00:00:46.332
It crosses zero exactly at the solutions we found.

13
00:00:47.132 --> 00:00:51.602
So the answer is x equals negative 2 or x equals 3.

14
00:00:52.052 --> 00:00:58.205
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

15
00:00:59.005 --> 00:01:06.517
x equals negative 2: left side equals negative 3, right side equals negative 3, which checks out.

16
00:01:06.967 --> 00:01:12.830
x equals 3: left side equals 2, right side equals 2, which checks out.