Lesson 13.2: Completing the Square — Practice Questions

1. 1. What value must be added to the expression $x^2 + 18x$ to make it a perfect square trinomial? ___

2. 2. Which expression is the perfect square trinomial formed by completing the square for $y^2 - 14y$?

   • A. $y^2 - 14y - 49$
   • B. $y^2 - 14y + 196$
   • C. $y^2 - 14y + 49$
   • D. $y^2 - 14y + 7$

3. 3. To complete the square for the expression $z^2 + 7z$, the number ___ must be added. (Enter as a fraction)

4. 4. After completing the square for $x^2 + 16x$, what is the factored form of the resulting trinomial?

   • A. $(x+8)^2$
   • B. $(x+16)^2$
   • C. $(x+4)^2$
   • D. $(x+64)^2$

5. 5. The expression $p^2 - 22p + 121$ is a perfect square trinomial. What is its factored form? ___

6. 6. Solve the equation $p^2 + 6p = -11$ by completing the square.

   • A. $p = 3 \pm i\sqrt{2}$
   • B. $p = -3 \pm 2i$
   • C. $p = -3 \pm i\sqrt{2}$
   • D. $p = 3 \pm \sqrt{2}$

7. 7. Solve the equation $(x + 2)(x + 4) = 3$ by completing the square.

   • A. $x = -5, x = -1$
   • B. $x = 1, x = 5$
   • C. $x = -2, x = -4$
   • D. $x = -3 \pm \sqrt{5}$

8. 8. Solve the equation $(x + 6)(x - 2) = 9$ by completing the square.

   • A. $x = -7, x = 3$
   • B. $x = -3, x = 7$
   • C. $x = -2 \pm \sqrt{21}$
   • D. $x = -2 \pm 5$

9. 9. Solve the equation $n^2 - 2n = -3$ by completing the square.

   • A. $n = -1 \pm i\sqrt{2}$
   • B. $n = 1 \pm 2i$
   • C. $n = 1 \pm i\sqrt{2}$
   • D. $n = -1 \pm \sqrt{2}$

10. 10. Solve the equation $l^2 - 10l - 6 = 5$ by completing the square.

    • A. $l = -1, l = 11$
    • B. $l = 1, l = -11$
    • C. $l = 5 \pm \sqrt{11}$
    • D. $l = -5 \pm 6$