Answer: It might work, but before you do that I would suggest you try to analyze why the grass is not growing there in particular (assuming it is growing okay in the rest of your yard.) Grass jsut will not grow in deep shade, or under trees, or where there are extensive surface roots from nearby trees. It will not grow in extremely dry spots such as on a steep hill, or in areas where there is bedrock just below the surface causing the soil to dry out quickly and allowing little space for grass roots.
Sometimes there is a less obvious reason. There may be a problem with the topsoil in that portion of your yard if it was brought in from a different source. Someone at one time may have had a dog run there, causing the soil to be severely compacted. Or something may have been applied to the soil there to prevent grass growth -- such as a long lasting herbicide, oil from parked cars, extreme over fertilization or over application of lime, or some other unusual situation.
Generally speaking, grass grows best in full sun all day or at least a half a day, the soil should be loosened down about six inches and fertilizer or lime added as indicated by soil test results, plus organic matter such as compost should be worked into the soil. Then you would plant seed or install sod. The best time of year to do this is actually late summer to early fall.
At this point, I would suggest you begin by running some basic soil tests and trying to determine why the lawn is not succeeding in that area. Your local county extension should be able to help you with the testing and interpreting the results. They should also be able to help you trouble shoot. Finally, they should also be able to recommend the best grass seed variety to plant in that spot.
I hope this helps!
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