WEBVTT

1
00:00:00.000 --> 00:00:05.352
Here is the problem: 8x squared minus 24x plus 10 equals 0.

2
00:00:05.802 --> 00:00:09.889
A quadratic equation in x: solve with the quadratic formula.

3
00:00:10.689 --> 00:00:12.233
Start with the equation.

4
00:00:12.683 --> 00:00:15.992
Move every term to one side to get standard form.

5
00:00:16.442 --> 00:00:17.824
Compute the discriminant.

6
00:00:18.274 --> 00:00:22.419
delta greater than 0, so there are two distinct real roots.

7
00:00:23.219 --> 00:00:24.960
Apply the quadratic formula.

8
00:00:25.411 --> 00:00:27.060
Simplify each root.

9
00:00:27.510 --> 00:00:28.590
Factored form.

10
00:00:29.390 --> 00:00:34.115
So the answer is x equals 1 over 2 or x equals 5 over 2.

11
00:00:34.565 --> 00:00:40.776
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

12
00:00:41.576 --> 00:00:48.890
x equals 0.5: left side equals 0, right side equals 0, which checks out.

13
00:00:49.340 --> 00:00:57.188
x equals 2.5: left side equals 0, right side equals 0, which checks out.