Complete the square, and solve by completing the square

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Noah solves 2x² + 4x = 96 by completing the square. What is the larger solution?

   6
2. 2.

   Pia's robot solves 2x² - 4x = 96, one step at a time. What is the smaller solution?

   -6
3. 3.

   In math club, Tala solves 2x² + 12x = 14. What is the smaller solution?

   -7
4. 4.

   Ari solves x² + 5x = 2 (halves are allowed). What is the smaller solution, to the nearest tenth?

   -5.4
5. 5.

   Bo's robot solves x² - 7x = 3 and rounds at the very end. What is the larger solution, to the nearest tenth?

   7.4
6. 6.

   In math club, Esme solves x² - x = 4. What is the smaller solution, to the nearest tenth?

   -1.6
7. 7.

   Jun rewrites 2x² - 12x + 7 as 2(x - 3)² + k. What is k?

   -11
8. 8.

   Luz rewrites 3x² + 12x + 5 as 3(x + 2)² + k to find the lowest row. What is k?

   -7
9. 9.

   Milo's robot rewrites 2x² + 20x + 9 as 2(x + 5)² + k. What is k?

   -41
10. 10.

    In math club, Noah rewrites 4x² - 8x + 1 as 4(x - 1)² + k. What is k?

    -3