WEBVTT

1
00:00:00.000 --> 00:00:05.457
Here is the problem: 2x squared minus 9x plus 3 equals 0.

2
00:00:05.907 --> 00:00:10.226
A quadratic equation in x: solve with the quadratic formula.

3
00:00:11.026 --> 00:00:12.512
Start with the equation.

4
00:00:12.962 --> 00:00:16.050
Move every term to one side to get standard form.

5
00:00:16.500 --> 00:00:17.916
Compute the discriminant.

6
00:00:18.366 --> 00:00:22.325
delta greater than 0, so there are two distinct real roots.

7
00:00:23.125 --> 00:00:24.843
Apply the quadratic formula.

8
00:00:25.293 --> 00:00:27.058
Simplify the square root.

9
00:00:27.508 --> 00:00:28.750
Reduce the fraction.

10
00:00:29.550 --> 00:00:47.081
So the answer is x equals (9 minus the square root of 57 over 4 approximately 0.36254139 or x equals (9 plus the square root of 57 over 4 approximately 4.1374586.

11
00:00:47.531 --> 00:00:53.394
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

12
00:00:54.194 --> 00:01:03.900
x equals 0.36254139: left side equals 0, right side equals 0, which checks out.

13
00:01:04.350 --> 00:01:13.197
x equals 4.1374586: left side equals 0, right side equals 0, which checks out.