Answer: Congratulations on your tomatoes! As for the carrots, root crops need a rich, loose, well-drained soil. Many of the areas in the Phoenix area have dense, hard-packed clay. I've added some info below on soil improvement. Make sure the soil is loose and deep enough so roots have plenty of room to grow. You might want to consider raised beds for your root crops. Add a phosphorous source to the soil before planting, as root crops benefit from that.
Spacing is another important aspect for root crops. Sometimes it's hard for gardeners to thin plants, but if you want big carrots you need to pull out seedlings as they grow. Finally, when are you planting the carrots? They are a cool-season crop in the low desert and are best sown from September through April. A good reference book that contains planting calendars for the low desert is called "Desert Gardening for Beginners: How to Grow Vegetables, Flowers and Herbs in an Arid Climate." ISBN 0-9651987-2-3.
To improve your soil, incorporate plenty of compost. In sandy soils, compost improves soil fertility, water and nutrient retention. In clay soils, it improves fertility and drainage. Add a 4-6 inch layer of compost and incorporate it about 12-18 inches deep. You can use manure if it is well-aged (6 months) or you won't be planting until it has lost it's heat and decomposed. Each planting season, add more compost. Incorporate a balanced fertilizer (e.g., 10-10-10) or add organic fertilizers such as fish emulsion, bone meal, and seaweed/kelp. Follow package instructions. I hope this info helps!
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