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Solving Quadratic Equations Practice Problems

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Updated on Aug 24, 2011

To review these concepts, go to Solving Quadratic Equations Study Guide.

Practice

Solve the quadratic equations using factoring.

  1. a2 + 2a – 24 = 0
  2. b2b – 6 = 0
  3. x2 + 15x + 50 = 0
  4. y2 – 8y + 7 = 0
  5. r2 + 12r + 27 = 0
  6. x2 + 8x – 48 = 0
  7. x2 + 7x – 18 = 0
  8. x2 + 4x = 45
  9. x2 – 6 = 30 – 3x2
  10. x2 + 11x = – 24
  11. 2x2 – 16x – 18 = 0
  12. 6x2 – 12x + 6 = 0
  13. x2 – 4x = 45
  14. 2x2 – 5x – 7 = 0
  15. 3x2 – 20x= 7
  16. 2x2 + 2x – 4 = 0
  17. x2 + 2x = 15
  18. 2x2 + 6x – 20 = 0
  19. 16x2 + 2x = 2x + 9
  20. 15x2 + 84x = 36

Applications Practice

  1. A rectangle is 6 feet wide and 4 feet tall. What amount should be added to the height and width to make the area 63 square ft.?
  2. The Jensens are installing a swimming pool in their backyard. The dimensions of the pool are 25 ft. by 30 ft. They want to have a sidewalk around the pool, but the area of the pool and the sidewalk must be 1,050 square ft. What is the length that should be added to each side of the pool to get an area of 1,050 square ft.? What will be the width of the sidewalk?
  3. Jessica is making a quilt. Each quilting square is 4 inches by 4 inches. She wants to put a border around each square so that the new area of the quilting square will be 36 square inches. What length does she have to add to each side? What is he width of the border?
  4. A dairy is required to have a waste holding pond for runoff. Ms.Van Beek plans to build a pond that will be 20 ft. by 15 ft. There will be a border of equal length around the pond. The total area of the pond and the border is 500 square ft. How wide will the border be?
  5. Mr. Ingram wants to add a garage to his home. The dimensions of his home are 50 ft. by 20 ft. When securing his building permit, he found that his home with the garage cannot be more than 1,400 square ft. How long can he extend the side of his house that is 50 ft. long so that his remodeling project will follow the code?

Solutions

  1. –6,4
  2. 3,–2
  3. –10,–5
  4. 7,1
  5. –9,–3
  6. –12,4
  7. –9,2
  8. –9,5
  9. –3,3
  10. –8,–3
  11. 9,–1
  12. 1,1
  13. 9,–5
  14. –2,1
  15. –5,3
  16. 2,–5
  17. 3 ft.
  18. 2 in. for the added length, 1 in. for the width of the border
  19. 20 ft.
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