WEBVTT

1
00:00:00.000 --> 00:00:05.178
Here is the problem: sqrt(x plus 3) equals x minus 3.

2
00:00:05.628 --> 00:00:11.154
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.954 --> 00:00:13.428
Start with the equation.

4
00:00:13.878 --> 00:00:15.863
Rewrite as f(x) equals 0.

5
00:00:16.313 --> 00:00:32.637
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
00:00:33.087 --> 00:00:38.312
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:39.111 --> 00:00:41.630
So the answer is x equals 6.

8
00:00:42.080 --> 00:00:50.532
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:51.332 --> 00:00:57.532
x equals 6: left side equals 3, right side equals 3, which checks out.