WEBVTT

1
00:00:00.000 --> 00:00:04.168
Here is the problem: sqrt(x) plus 2 equals x.

2
00:00:04.618 --> 00:00:10.226
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:11.026 --> 00:00:12.524
Start with the equation.

4
00:00:12.974 --> 00:00:15.122
Rewrite as f(x) equals 0.

5
00:00:15.572 --> 00:00:31.710
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
00:00:32.160 --> 00:00:37.210
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:38.010 --> 00:00:40.274
So the answer is x equals 4.

8
00:00:40.724 --> 00:00:49.571
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:50.371 --> 00:00:56.989
x equals 4: left side equals 4, right side equals 4, which checks out.