# 9.2E: Exercises

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### Practice Makes Perfect

##### ExerciseS 1 - 4: Complete the Square of a Binomial Expression

In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.

1. $$m^{2}-24 m$$
2. $$x^{2}-11 x$$
3. $$p^{2}-\frac{1}{3} p$$
1. $$n^{2}-16 n$$
2. $$y^{2}+15 y$$
3. $$q^{2}+\frac{3}{4} q$$
1. $$p^{2}-22 p$$
2. $$y^{2}+5 y$$
3. $$m^{2}+\frac{2}{5} m$$
1. $$q^{2}-6 q$$
2. $$x^{2}-7 x$$
3. $$n^{2}-\frac{2}{3} n$$

1. a. $$(m-12)^{2}$$ b. $$\left(x-\frac{11}{2}\right)^{2}$$ c. $$\left(p-\frac{1}{6}\right)^{2}$$

3. a. $$(p-11)^{2}$$ b. $$\left(y+\frac{5}{2}\right)^{2}$$ c. $$\left(m+\frac{1}{5}\right)^{2}$$

##### ExerciseS 5 - 28: Solve Quadratic Equations of the Form $$x^{2}+b x+c=0$$ by Completing the Square

In the following exercises, solve by completing the square.

5. $$u^{2}+2 u=3$$

6. $$z^{2}+12 z=-11$$

7. $$x^{2}-20 x=21$$

8. $$y^{2}-2 y=8$$

9. $$m^{2}+4 m=-44$$

10. $$n^{2}-2 n=-3$$

11. $$r^{2}+6 r=-11$$

12. $$t^{2}-14 t=-50$$

13. $$a^{2}-10 a=-5$$

14. $$b^{2}+6 b=41$$

15. $$x^{2}+5 x=2$$

16. $$y^{2}-3 y=2$$

17. $$u^{2}-14 u+12=-1$$

18. $$z^{2}+2 z-5=2$$

19. $$r^{2}-4 r-3=9$$

20. $$t^{2}-10 t-6=5$$

21. $$v^{2}=9 v+2$$

22. $$w^{2}=5 w-1$$

23. $$x^{2}-5=10 x$$

24. $$y^{2}-14=6 y$$

25. $$(x+6)(x-2)=9$$

26. $$(y+9)(y+7)=80$$

27. $$(x+2)(x+4)=3$$

28. $$(x-2)(x-6)=5$$

5. $$u=-3, u=1$$

7. $$x=-1, x=21$$

9. $$m=-2 \pm 2 \sqrt{10} i$$

11. $$r=-3 \pm \sqrt{2} i$$

13. $$a=5 \pm 2 \sqrt{5}$$

15. $$x=-\frac{5}{2} \pm \frac{\sqrt{33}}{2}$$

17. $$u=1, u=13$$

19. $$r=-2, r=6$$

21. $$v=\frac{9}{2} \pm \frac{\sqrt{89}}{2}$$

23. $$x=5 \pm \sqrt{30}$$

25. $$x=-7, x=3$$

27. $$x=-5, x=-1$$

##### ExerciseS 29 - 40: Solve Quadratic Equations of the Form $$a x^{2}+b x+c=0$$ by Completing the Square

In the following exercises, solve by completing the square.

29. $$3 m^{2}+30 m-27=6$$

30. $$2 x^{2}-14 x+12=0$$

31. $$2 n^{2}+4 n=26$$

32. $$5 x^{2}+20 x=15$$

33. $$2 c^{2}+c=6$$

34. $$3 d^{2}-4 d=15$$

35. $$2 x^{2}+7 x-15=0$$

36. $$3 x^{2}-14 x+8=0$$

37. $$2 p^{2}+7 p=14$$

38. $$3 q^{2}-5 q=9$$

39. $$5 x^{2}-3 x=-10$$

40. $$7 x^{2}+4 x=-3$$

29. $$m=-11, m=1$$

31. $$n=1 \pm \sqrt{14}$$

33. $$c=-2, c=\frac{3}{2}$$

35. $$x=-5, x=\frac{3}{2}$$

37. $$p=-\frac{7}{4} \pm \frac{\sqrt{161}}{4}$$

39. $$x=\frac{3}{10} \pm \frac{\sqrt{191}}{10} i$$

##### ExerciseS 41 - 42: writing exercises

41. Solve the equation $$x^{2}+10 x=-25$$

1. by using the Square Root Property
2. by Completing the Square
3. Which method do you prefer? Why?

42. Solve the equation $$y^{2}+8y=48$$ by completing the square and explain all your steps.