Sole the equation 2^x - x = 5

Question

gingy57016 · Answer

at first you combine the like terms

Spectrum · Answer

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:

Luigi0210 · Answer

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} $