No need to blow it out!
Photographers are often called on to provide a portrait or a product photo against a clean white background. It is a nice clean look. But it can go bad quickly if you aren't careful. You can go from a clean, crisp, and sharp image to one with muddy edges, lowered contrast, and lots of flare.
So, just how white do you need to make the backdrop? Let's start with the backdrop. My choice is Savage Universal seamless paper. Savage offers three different white papers. White, Pure White, and Super White. Of these, I prefer Pure White. "Regular" white is a bit on the warm side. Super White has extra brighteners and might go a bit to the blue side in some situations. Pure White tends to stay neutral in various lighting setups.
Now that we have the backdrop selected we have to decide if we need to light it separately from the subject, and if so, how to light it. In many situations we are going to want to light the backdrop to keep it white and not turn gray. For individual subjects we can often get by using one light on the background. For groups we will probably need two lights, one from each side.
With that choice out of the way, we need to figure out how to expose the background. I've seen online discussions where the "experts" say to make the background 2 stops brighter than the subject to make sure the background goes white. Please don't do that!! The paper is already white, so in theory it could get the same amount of light as the subject and be white. For a little bit of insurance, you can overexpose the white background by 1/3 to 1/2 stop brighter than the light on the subject. Once you go past that you can easily have too much light bouncing back off the background and washing out the edges of the subject, especially their hair. A little bit more exposure and there is an overall haze and loss of contrast. If this is the look you want, then go for it! But in many situations this is a recipe for failure. Let's look at this series of images. All are photographed on white seamless with a 2x3-foot softbox on the subject (yours truly) and a separate light with a 7-inch metal dish reflector on the backdrop.
For each image I took a meter reading at the subject and at another reading at the backdrop. In the first image both read f/10. I added a white border on each side of the photos and you can see that in the first image the background is close to but not pure white. And yes, I let the backdrop fall off from left side to right. I could have pulled the background light farther away from the paper to make it more even, but I was more interested in showing the effects of exposure. The second image has the background reading f/13, which is 2/3 of a stop brighter than the subject. Here you can see that the background on the left side of the image is now almost as white as the border, but there is still good contrast in the image. Strands of flyaway hair can still be seen. If you had to, you could easily brighten the background a touch in Lightroom or Photoshop to be as white as the border.