00:01
All right, we've got a rectangle.
00:05
It's got a length and a width, and the area is 10 square feet, and the formula for area is length time width.
00:14
But we also are told that the width could be found by doing the length minus 12.
00:20
So when we write this, we can replace the width with the length minus 12, and it turns out that we get 10 equals l squared minus 12 l.
00:33
Now, that's a quadratic equation that we're going to need to solve, and we can use the quadratic formula, which says the opposite of b plus or minus the square root of b squared minus 4a, all over 2a.
00:46
All right, so this needs to be set equal to zero.
00:49
Let's move this 10 over, so we get l squared 12l minus 10.
00:55
So when we plug into the quadratic formula, we get a is 1, b is negative 12, and c is negative 10.
01:03
So over here, let's look for l.
01:05
We have the opposite of b, which is positive 12, plus or minus the square root of b squared times, or b squared minus 4 times a times a, that all ends up being 184, all over 2 times a, 2 times 1 here is 2.
01:21
We can do some simplification on this.
01:25
The square root of 184 is going to be two square roots of 46.
01:32
And when we divide these things by two, l ends up being six plus or minus the square root of 46.
01:40
All right.
01:41
So that is our exact answer, which means the width is going to be six plus or minus.
01:51
Hold on, we got to go back because we need to address this because it's not going to be two answers.
01:56
All right...