Factoring Worksheet1 Solution8

In this page factoring worksheet1 solution8 we are going to see solution of some practice questions from factoring worksheet1.

Question 5:

Solve by completing the square method x² – (3 + 1) x + √3 = 0

Solution:

x² – 2 (x)((√3 + 1)/2) + [((3 + 1)/2)]² - [((3 + 1)/2)]²+ √3 = 0

[x –  (3 + 1)/2)]² =  [((3 + 1)/2)]²- 3 = 0

[x –  (3 + 1)/2)]² =  [3² + 12 + 2(3 )1/4)]- √3

[x –  (3 + 1)/2)]² =  [3² + 12 + 2(3)- 43]/4

[x –  (3 + 1)/2)]² =  [3² + 12 - 2(3)]/4

[x –  (3 + 1)/2)]² =  [(3 – 1)/2]²

[x –  (3 + 1)/2)] = [(3 – 1)/2]²

[x –  (3 + 1)/2)] = ± [(3 – 1)/2]

x = ± [(3 – 1)/2] + (3 + 1)/2)]

x =  [(3 – 1)/2] + (3 + 1)/2)]              x = - [(3 – 1)/2] + (3 + 1)/2)]

x = (3 – 1 + 3 + 1)/2)                               x = (-3 + 1+3 + 1)/2

x = 23/2                                                       x = 2/2

x = 3                                                               x = 1

Verification:

x² – (3 + 1) x + √3 = 0

if x = 3

3² – (3 + 1)3  + √3 = 0

3 - 3 - 3 + 3 = 0

0 = 0

if x = 1

1² – (3 + 1)1  + √3 = 0

1 - 3 - 1 + 3 = 0

0 = 0                factoring worksheet1 solution8

Question 6:

Solve by completing the square method (5 x + 7)/(x – 1) = 3 x + 2

Solution:

(5 x + 7) = (3 x + 2)(x – 1)

5 x + 7 = 3 x² – 3 x + 2 x – 2

3 x² – 3 x + 2 x – 2 – 5x – 7 = 0

3 x² – 8 x + 2 x – 9 = 0

3 x² – 6 x – 9 = 0

Now we are going to divide the whole equation by 3

x² – 2 x – 3 = 0

x² – 3 x + x – 3 = 0

x (x – 3) + 1 (x – 3) = 0

(x – 3)(x + 1) = 0

x – 3 = 0                 x + 1 = 0

x = 3                       x = -1

Verification:

(5 x + 7)/(x – 1) = 3 x + 2

if x = 3

[5 (3) + 7]/(3-1) = 3 (3) + 2

(15 + 7)/2 = 9 + 2

22/2 = 11

11 = 11

if x = -1

(5 x + 7)/(x – 1) = 3 x + 2

(5 (-1) + 7)/((-1) – 1) = 3 (-1) + 2

(-5 + 7)/(-2) = -3 + 2

2/(-2) = -1

- 1 = -1

factoring worksheet1 solution8 factoring worksheet1 solution8