COMPLETING THE SQUARE METHOD EXAMPLES WITH ANSWERS

Example 1 :

Solve by completing the square method 

x² – (√3 + 1)x + √3 = 0 

Solution :

x² – (√3 + 1)x + √3 = 0 

x² – (√3 + 1)x  =  -√3

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

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

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

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

[x - (√3 + 1)/2]²  =  [ (√3 - 1)/2 ]²

[x - (√3 + 1)/2]²  =  [ (√3 - 1)/2 ]²

[x - (√3 + 1)/2]  =  ± (√3 - 1)/2

Example 2 :

Solve by completing the square method 

(5x + 7)/(x – 1)  =  3x + 2

Solution :

(5x + 7)  =  (3x + 2)(x – 1)

5x + 7  =  3x² – 3x + 2x – 2

3x² – 3x + 2x – 2 – 5x – 7  =  0

3x² – 6x – 9  =  0

Divide the entire equation by 3, we get

x² – 2x – 3  =  0

x² – 3x + x – 3  =  0

x (x – 3) + 1 (x – 3)  =  0

(x – 3)(x + 1)  =  0

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