Solving using completing the square (answers) Textbook Answers

Workout

Question 1:

(a) x = -2 or x = -4 (b) x = -6 or x = -4 (c) x = -4 or x = -10

(d) x = -5 or x = 9 (e) x = 5 or x = 7 (f) x = -1 or x = 3

(g) x = -17 or x = 3 (h) x = -2 or x = 8 (i) x = 1

Question 2:

(a) x = -4 or x = -1 (b) x = -3 or x = 6 (c) x = -4 or x = 3

(d) x = 3 or x = 4 (e) x = 3 or x = 8 (f) x = -3 or x = 10

Question 3:

(a) x = -2 + √7 or x = -2 – √7

(b) x = -3 + √19 or x = -3 – √19

(d) x = 5 + 2√6 or x = 5 – 2√6 (note √24 = 2√6)

(e) x = -4 + √13 or x = -4 – √13

(f) x = 4 + √38 or x = 4 – √38

(g) x = -10 + √93 or x = -10 – √93

(h) x = 6 + √35 or x = 6 – √35

(i) x = 15 + 5√13 or x = 15 – 5√13 (note √325 = 5√13)

Question 4:

(a) x = -1/2 + √29/2 or x = -1/2 – √29/2

(b) x = 3/2 + √5/2 or x = 3/2 – √5/2

(d) x = 7/2 + √13/2 or x = 7/2 – √13/2

(e) x = 1/2 + √201/2 or x = 1/2 – √201/2

(f) x = -13/2 + √165/2 or x = -13/2 – √165/2

Question 5:

(a) x = 2 – √13 or x = 2 + √13

(b) x = -5 + 2√10 or x = -5 – 2√10

(d) x = -1 + √6 or x = -1 – √6

(e) x = -5 + √37 or x = -5 – √37

(f) x = -1 – √14 or x = -1 + √14

Question 6:

(a) x = -3 + √11 or x = -3 – √11

(b) x = -3 or x = -0.5

(d) x = 3/4 + √65/4 or x = 3/4 – √65/4

(e) x = -1/5 + √41/5 or x = -1/5 – √41/5

(f) x = 1/10 + √11/10 or x = 1/10 – √11/10

Apply

Question 1: (a) (0, 3) (b) (-5+√22, 0) and (-5-√22, 0)

Question 2: width = -10 + 10√11 cm and length = 10 + 10√11 cm

Question 3: When solving using completing the square, Abby will get to the point (x+2)^2 = -11. She will need to √-11, which has no solutions (real ones anyway!)

Question 4: 5√17

Question 5: a = 6 and b = -8

Question 6: https://corbettmaths.com/2015/03/19/deriving-the-quadratic-formula/

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Solving using completing the square (answers) Textbook Answers