Complete the square, and solve by completing the square

Answer Key - Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Milo arranges tiles for x² + 10x: one x-by-x square plus 10 thin strips, split along two sides. What number fills the corner, so x² + 10x + ? is a perfect square?

   25
2. 2.

   Noah plans a square quilt from x² + 16x: one big patch plus strips along two sides. What number fills the corner, so x² + 16x + ? is a perfect square?

   64
3. 3.

   Pia draws x² - 6x as a square on paper, with a corner left empty. What number fills the corner, so x² - 6x + ? is a perfect square?

   9
4. 4.

   Ren's square rug design is x² - 20x, with one corner still missing. What number fills the corner, so x² - 20x + ? is a perfect square?

   100
5. 5.

   Zee's puzzle card shows x² - 18x + 81. Which shows it written as a perfect square?

   • (x - 9)(x + 9)
   • (x - 18)²
   • (x + 9)²
   • (x - 9)²
6. 6.

   Ari sews a square quilt modeled by x² + 22x + 121. Which shows it written as a perfect square?

   • (x + 11)²
   • (x + 11)(x - 11)
   • (x + 22)²
   • (x - 11)²
7. 7.

   Bo's robot factors x² - 24x + 144 (it likes tidy squares). Which shows it written as a perfect square?

   • (x - 12)²
   • (x - 12)(x + 12)
   • (x + 12)²
   • (x - 24)²
8. 8.

   Esme solves x² + 6x = 7 by completing the square. The same number goes on both sides, so the left becomes (x + 3)². What number is on the right?

   16
9. 9.

   Jun works on x² + 10x = 11 with a sharp pencil. The same number goes on both sides, so the left becomes (x + 5)². What number is on the right?

   36
10. 10.

    Kira solves x² - 4x = 12 with algebra tiles. The same number goes on both sides, so the left becomes (x - 2)². What number is on the right?

    16