Fortunately, there's a little trick you can use to smooth out those jaggies fairly quickly in the majority of image editing software. In this tutorial, I'll show you how using the free photo editor, Paint.NET, but you can adapt this tutorial to use another image editor as long as it has a Gaussian blur filter and a curves or levels adjustment tool. These are fairly standard tools in any image editor.
Save the sample image to you computer if you'd like to follow along with this tutorial.
Start by opening Paint.NET, then choose the open button on the toolbar and open the sample image or another you'd like to work with.
Note: Since Paint.NET is only designed to work with 32-bit images, any image you open is converted to 32-bit RGB color mode. If you are using another image editor and your image is in a reduced-color format such as GIF or BMP, you will first need to convert your image to an RGB color image. Consult your software's help files for information on how to change the color mode of an image.