9.3E: Exercises
Practice Makes Perfect
In the following exercises, complete the square to make a perfect square trinomial. Then write the result as a binomial squared.
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- \(m^{2}-24 m\)
- \(x^{2}-11 x\)
- \(p^{2}-\frac{1}{3} p\)
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- \(n^{2}-16 n\)
- \(y^{2}+15 y\)
- \(q^{2}+\frac{3}{4} q\)
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- \(p^{2}-22 p\)
- \(y^{2}+5 y\)
- \(m^{2}+\frac{2}{5} m\)
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- \(q^{2}-6 q\)
- \(x^{2}-7 x\)
- \(n^{2}-\frac{2}{3} n\)
- Answer
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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. \(\left(m+\frac{1}{5}\right)^{2}\)
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. \((x-2)(x-6)=5\)
- Answer
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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. \(x=-5, x=-1\)
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. \(7 x^{2}+4 x=-3\)
- Answer
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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. \(x=\frac{3}{10} \pm \frac{\sqrt{191}}{10} i\)
41. Solve the equation \(x^{2}+10 x=-25\)
- by using the Square Root Property
- by Completing the Square
- Which method do you prefer? Why?
42. Solve the equation \(y^{2}+8y=48\) by completing the square and explain all your steps.
- Answer
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41. Answers will vary
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. After reviewing this checklist, what will you do to become confident for all objectives?