WEBVTT

1
00:00:00.000 --> 00:00:04.005
Here is the problem: x plus 1/x equals 2.

2
00:00:04.455 --> 00:00:08.611
A quadratic equation in x: solve with the quadratic formula.

3
00:00:09.411 --> 00:00:10.874
Start with the equation.

4
00:00:11.324 --> 00:00:21.738
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
00:00:22.188 --> 00:00:25.218
Move every term to one side to get standard form.

6
00:00:25.668 --> 00:00:27.050
Compute the discriminant.

7
00:00:27.850 --> 00:00:31.530
delta equals 0, so there is one repeated real root.

8
00:00:31.980 --> 00:00:33.745
Apply the quadratic formula.

9
00:00:34.195 --> 00:00:35.252
Factored form.

10
00:00:36.052 --> 00:00:40.069
Now look at the graph of the left side minus the right side.

11
00:00:40.519 --> 00:00:44.304
It crosses zero exactly at the solutions we found.

12
00:00:45.104 --> 00:00:47.995
So the answer is x equals 1 (double root).

13
00:00:48.445 --> 00:00:54.784
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

14
00:00:55.584 --> 00:01:01.935
x equals 1: left side equals 2, right side equals 2, which checks out.