Solve the equation for x: x² - 4 = 2^(x - 5)?
x^2 - 4 = 2x-10
x^2-2x+6 = 0
There you go... solve by factor or that quadratic formula.
If I read your equation correctly, you said:
x2 - 4 = 2x-5
If that is the case, then the solution is much more complicated than Jake1214 has suggested.
I ran it through my trusty homemade "Newton Method" equation solver and got approximate answers of
x = 2.031693
x = -2.001951
and another answer between x = 12.1 and 12.2 (it kept giving me an overflow error if I tried to refine the domain, I wrote my program in an archaic version (1970's) of GWBasic)
If you make a rough graph of
f(x) = x^2 - 4 - 2^(x-5), it will verify that.
To solve the equation x² - 4 = 2^(x - 5), we need to find the value(s) of x that satisfy the equation. However, this equation does not have an explicit solution that can be found algebraically. Instead, we can use numerical methods or approximation techniques to estimate the value(s) of x that make the equation true.
One approach to solve this equation is by using a graphing calculator or computer software to plot the two functions and find their point(s) of intersection. Here's how you can do it:
1. Rewrite the equation as a function: f(x) = x² - 4 - 2^(x - 5).
2. Use a graphing calculator or computer software to plot the graphs of f(x) and g(x) = 0 on the same coordinate system.
3. Look for the point(s) of intersection between the two graphs. These points represent the value(s) of x that satisfy the equation.
Alternatively, you can use an iterative method, such as the Newton-Raphson method or the bisection method, to approximate the solutions. These methods rely on repeatedly refining an initial estimate until it converges to a more accurate solution. However, implementing these methods can be complex and is usually done using programming languages or dedicated software.
Therefore, in this case, it is recommended to use a graphing calculator or computer software to find the approximate value(s) of x that satisfy the equation x² - 4 = 2^(x - 5).