Answer: Unfortunately, the product you used contains glyphosate as the active ingredient. This is a nonselective herbicide meaning it will kill all plants including lawn grass, not just the weeds you want to kill. You will need to reseed the bare spots.
The best defense against weeds is a healthy turf. Correct mowing keeps the lawn grass dense and helps it crowd out weeds. Mow to a height of three inches; mow often enough that you do not remove more than one third the grass height when you cut it.
Next, run some basic soil tests to check fertility and soil pH. Use the soil test results to know how much to fertilize and if you need to add lime as well.
Healthy lawn can crowd out many annual weeds and some perennial weeds over time. Perennial weeds can be spot treated with glyphosate, or dug out by hand. Your local county extension can help you with the soil testing and interpreting the results as well as help develop a lawn care plan for your yard.
You may also find the following lawn care information helpful.
Good luck with your lawn this summer!
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