WEBVTT

1
00:00:00.000 --> 00:00:05.248
Here is the problem: 4x squared minus 12x plus 9 equals 0.

2
00:00:05.698 --> 00:00:09.762
A quadratic equation in x: solve with the quadratic formula.

3
00:00:10.562 --> 00:00:12.095
Start with the equation.

4
00:00:12.544 --> 00:00:15.690
Move every term to one side to get standard form.

5
00:00:16.140 --> 00:00:17.603
Compute the discriminant.

6
00:00:18.053 --> 00:00:21.919
delta equals 0, so there is one repeated real root.

7
00:00:22.719 --> 00:00:24.437
Apply the quadratic formula.

8
00:00:24.887 --> 00:00:25.955
Factored form.

9
00:00:26.755 --> 00:00:30.296
So the answer is x equals 3 over 2 (double root).

10
00:00:30.746 --> 00:00:36.934
The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

11
00:00:37.734 --> 00:00:44.955
x equals 1.5: left side equals 0, right side equals 0, which checks out.