WEBVTT

1
00:00:00.000 --> 00:00:05.677
Here is the problem: 4x squared minus 12x minus 39 equals 0.

2
00:00:06.127 --> 00:00:10.121
A quadratic equation in x: solve with the quadratic formula.

3
00:00:10.921 --> 00:00:12.395
Start with the equation.

4
00:00:12.845 --> 00:00:15.805
Move every term to one side to get standard form.

5
00:00:16.256 --> 00:00:17.626
Compute the discriminant.

6
00:00:18.076 --> 00:00:22.221
delta greater than 0, so there are two distinct real roots.

7
00:00:23.021 --> 00:00:24.762
Apply the quadratic formula.

8
00:00:25.213 --> 00:00:26.908
Simplify the square root.

9
00:00:27.358 --> 00:00:28.612
Reduce the fraction.

10
00:00:29.412 --> 00:00:47.849
So the answer is x equals (3 minus 4the square root of 3 over 2 approximately negative 1.9641016 or x equals (3 plus 4the square root of 3 over 2 approximately 4.9641016.

11
00:00:48.299 --> 00:00:54.371
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

12
00:00:55.171 --> 00:01:04.935
x equals negative 1.9641016: left side equals 0, right side equals 0, which checks out.

13
00:01:05.385 --> 00:01:14.545
x equals 4.9641016: left side equals 0, right side equals 0, which checks out.