## Textbook Answers – Completing the Square

July 27, 2016

Workout

Question 1

(a)  (x + 4)² – 15                  (b)  (x + 5)² – 22                     (c)  (x + 1)² – 2

(d)  (x – 3)² – 19                  (e)  (x – 2)² – 17                     (f)  (x – 6)² – 33

(g)  (x + 7)² – 46                 (h)  (x – 1)² – 16                     (i)  (x + 2)² – 15

(j)   (x + 0.5)² – 8.25          (k)  (x + 1.5)² – 1.25              (l)  (x – 3.5)² – 14.25

(m)  (x – 4.5)² – 21.25       (n)  (x + 5.5)² – 27.25          (o) (x – 50)² – 2525

Question 2

(a)  x = -2 + √3  or   x = -2 – √3

(b) x = -4 +√26  or  x = -4 – √26

(c)  x = -7 +√53   or  x = -7 – √53

(d)  x = 4 + 3√2   or   x = 4 – 3√2

(e)  x = 5 + √15   or    x = 5 – √15

(f)  x = -9 + √74   or   x = -9 – √74

(g)  x = -6 + 2√13   or    x = -6 – 2√13

(h)  x = 1 + √11   or   x = 1 – √11

(i)  x = 1/2 (7 + √61)    or   x = 1/2 (7 – √61)

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

(k)  No real roots

(l)  x = 3 + √39   or   x = 3 – √39

Question 3:

(a)  2(x + 2)² – 6                  (b)  2(x + 3)² – 21                  (c)    3(x – 2)² – 10

(d) 4(x + 1.5)² – 14              (e)  2(x – 0.75)² – 6.125       (f)   5(x – 2)² + 10

Question 4:

(a)  x = -2 + √3      or       x = -2 – √3

(b)  x = -4 + √26   or        x = -4 – √26

(c)  x =1/3 (3 + √6)  or   x = 1/3 (3 – √6)

(d)  x = 1/5 (-5 + √70)  or  x = 1/5(-5 – √70)

(e)  x = 3   or  x = -1/2

(f)  x = 1/4 (7 + √41)    or   x = 1/4(7 – √41)

Apply

Question 1:    x² + 6x + 5

Question 2:  x² -4x – 5

Question 3:  x² – 14x + 60

Question 4

(a)  (-5, -13)                (b) (-2, -3)               (c)  (-3, -1)                (d)  (1, 2)

(e)  (3, -12)                  (f)  (0.5, -4.25)       (g) (-4.5, -19.25)

(h)  (3, -11)                  (i)  (-11, -21)

Question 6:

Mistake 1 – it should be -25, not -10

Mistake 2 – if they added 2 to -10, it should be -8, not -12. It should be -25 + 2 = 23

Mistake 3 – they forgot the +/- in front of the √12, but it should be √23 anyway.

The correct answers should be:  x = -5 + √23  or  x = -5 – √23