How to get my Nikon d3100 to focus?

I hold the button half way down, and the image still looks blurry. When i take the picture, everything is still a blur. Why won't it focus the image?

Have you tried manual focus via the lense?

Have you adjusted the diopter at the view finder?
Look on page 22 of your user manual for more information
When you take a photo, does the image look in focus on your monitor?

Make sure your lens are set to AF instead of MF

Also, make sure you're not too close to your subject, as all lenses have a minimum focusing distance.

Make sure the AF switch on the lens is set to A not M. Turn the D3100 dial to AUTO to override other settings that you may have mistakenly set. Aim at a subject about 4 meters away. If it focuses correctly, you have problems with settings and its about time to read your user's manual.

Is your camera set on manual focus? Stand in a quiet area, and half-press the shutter button. If you hear a little whirring noise, then the auto-focus is switched on. If not, it is switched off.
If it's switched on, then possibly the particular subject you're shooting is hard for the camera to auto-focus on. This can happen when the subject is very plain (single colour with no contrast) or very close to the camera. Check that it's genuinely working by taking a photo of something with more contrast from further away.
If it's switched off, make sure the focus option (which I think is on the front of the camera, to the right of the lens as you look at it) is set to A. There may also (depending on which lend you're using) be another switch on the lens, set that to A as well.
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