WEBVTT

1
00:00:00.000 --> 00:00:05.770
Here is the problem: negative x squared minus x plus 42 equals 0.

2
00:00:06.220 --> 00:00:11.828
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:12.628 --> 00:00:14.149
Start with the equation.

4
00:00:14.599 --> 00:00:16.724
Rewrite as f(x) equals 0.

5
00:00:17.174 --> 00:00:33.347
This equation is not polynomial, so solve it numerically. Scan x from negative 10 to the power 9 to 10 to the power 9 for sign changes of f and for points where the graph touches the axis, then narrow each one down. Every root is checked by substituting it back.

6
00:00:33.797 --> 00:00:38.859
Found 2 solutions in [−10 to the power 9, 10 to the power 9].

7
00:00:39.659 --> 00:00:44.187
So the answer is x equals negative 7, x equals 6.

8
00:00:44.637 --> 00:00:53.437
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:54.237 --> 00:01:01.609
x equals negative 7: left side equals 0, right side equals 0, which checks out.

10
00:01:02.059 --> 00:01:08.723
x equals 6: left side equals 0, right side equals 0, which checks out.