WEBVTT

1
00:00:00.000 --> 00:00:05.596
Here is the problem: 12x squared minus 2x minus 11 equals 0.

2
00:00:06.046 --> 00:00:10.110
A quadratic equation in x: solve with the quadratic formula.

3
00:00:10.910 --> 00:00:12.315
Start with the equation.

4
00:00:12.765 --> 00:00:15.749
Move every term to one side to get standard form.

5
00:00:16.199 --> 00:00:17.569
Compute the discriminant.

6
00:00:18.019 --> 00:00:22.117
delta greater than 0, so there are two distinct real roots.

7
00:00:22.917 --> 00:00:24.635
Apply the quadratic formula.

8
00:00:25.085 --> 00:00:26.803
Simplify the square root.

9
00:00:27.253 --> 00:00:28.484
Reduce the fraction.

10
00:00:29.284 --> 00:00:48.928
So the answer is x equals (1 minus the square root of 133 over 12 approximately negative 0.87771355 or x equals (1 plus the square root of 133 over 12 approximately 1.0443802.

11
00:00:49.378 --> 00:00:55.496
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

12
00:00:56.296 --> 00:01:06.873
x equals negative 0.87771355: left side equals 0, right side equals 0, which checks out.

13
00:01:07.323 --> 00:01:17.029
x equals 1.0443802: left side equals 0, right side equals 0, which checks out.