WEBVTT

1
00:00:00.000 --> 00:00:05.155
Here is the problem: sqrt(x plus 9) equals x minus 4.

2
00:00:05.605 --> 00:00:11.131
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.931 --> 00:00:13.405
Start with the equation.

4
00:00:13.855 --> 00:00:15.980
Rewrite as f(x) equals 0.

5
00:00:16.430 --> 00:00:32.266
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
00:00:32.716 --> 00:00:37.720
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:38.520 --> 00:00:44.592
So the answer is x approximately 8.140054945.

8
00:00:45.042 --> 00:00:53.877
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:54.677 --> 00:01:10.803
x equals 8.1400549: left side equals 4.1400549, right side equals 4.1400549, which checks out.