Question

Sole the equation 2^x - x = 5

Answer 1

at first you combine the like terms

Answer 2

Nope, the first step is to move the normal x over to the side. Giving you 2^x = x + 5, any idea what you do next? c:

Answer 3

I'm going to assume you meant \(\large x^2\) and not \(\large 2^x\) because that will get messy.

To start off, you need to get everything to one side, so subtract 5:

\(\large x^2-x\color{red}{-5} = 0 \)

You can either try factoring, or using the quadratic formula:

\(\huge x = \frac{-(-1) \pm \sqrt{(-1)^2-4(1)(-5)}}{2(1)} \)

\(\Large x= \frac{1 \pm \sqrt{1+20}}{2} = \frac{1 \pm \sqrt{21}}{2} \)

Which can be simplified to:

\(\Large x = \frac{1 + \sqrt{21}}{2}, \frac{1 - \sqrt{21}}{2} \)