WEBVTT

1
00:00:00.000 --> 00:00:05.573
Here is the problem: sqrt(2x minus 1) equals x minus 2.

2
00:00:06.023 --> 00:00:11.573
Solve for x numerically (the equation contains functions such as sin, log or roots).

3
00:00:12.373 --> 00:00:13.917
Start with the equation.

4
00:00:14.367 --> 00:00:16.468
Rewrite as f(x) equals 0.

5
00:00:16.918 --> 00:00:33.253
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
00:00:33.703 --> 00:00:38.823
Found 1 solution in [−10 to the power 9, 10 to the power 9].

7
00:00:39.623 --> 00:00:41.980
So the answer is x equals 5.

8
00:00:42.430 --> 00:00:51.405
Values marked approximately are numerical approximations accurate to about 10 significant digits. Every value was checked by substitution.

9
00:00:52.204 --> 00:00:58.787
x equals 5: left side equals 3, right side equals 3, which checks out.