# COMPLETE THE SQUARE WORKSHEET

## About "Complete the square worksheet"

Complete the square worksheet :

Here we are going to see some practice question based on the concept completing the square method.

## Complete the square - Practice questions

(1)  Solve the quadratic equation  x² + 6 x - 7 = 0  by completing the square method

(2) Solve the quadratic equation  x² + 3 x + 1 = 0   by completing the square method

(3)  Solve the quadratic equation  2 x² + 5 x - 3  = 0 by completing the square method

(4)  Solve the quadratic equation  4 x² + 4 b x - (a² - b²) = 0  by completing the square method

(5)  Solve the quadratic equation    x² - ( √3 + 1) x + 3 = 0  by completing the square method

## Complete the square worksheet - Solution

Question 1 :

Solve the quadratic equation  x² + 6 x - 7 = 0  by completing the square method

Solution: (x + 3)² = 16

x + 3 = √ 16

x + 3 = ± 4

 x + 3 = 4 x  =  1 x + 3 = - 4  x  =  -7

Question 2 :

Solve the quadratic equation  x² + 3 x + 1 = 0   by completing the square method

Solution:

x² + 3 x + 1 = 0

x² + 3 x = -1

x² + 2 x (3/2) + (3/2)² = - 1 + (3/2)²

[x + (3/2)]² = - -1 + (9/4)

(x + (3/2))² = (9/4) - 1

(x + (3/2))² = (5/4)

(x + (3/2)) = √(5/4)

x + (3/2) = ± (√5/2)

 x + (3/2)  =  (√5/2)  x = (√5/2) - (3/2)    x = (√5 - 3)/2 x + (3/2)  =  -(√5/2) x = -(√5/2) - (3/2)   x = (-√5 - 3)/2

Question 3 :

Solve the quadratic equation  2 x² + 5 x - 3  = 0 by completing the square method

Solution:

2 x² + 5 x - 3  = 0

divide the whole equation by 2

x² + (5/2) x - (3/2) = 0

x² + (5/2) x = (3/2)

x² + 2 (5/2) x = (3/2)

x² + 2 x (5/2) + (5/2)² =  (5/2)²+ (3/2)

(x + (5/2))² - (25/4)- (3/2) = 0

(x + (5/2))² =  (25/4) + (3/2)

(x + (5/2))² =  (25 + 6)/4

(x + (5/2))² =  31/4

x + (5/2) = √(31/4)

x + (5/2) = ± √31/2

 x + (5/2) =  √31/2 x = (√31/2) - (5/2)  x = (√31 - 5)/2 x + (5/2) = -√31/2 x = (-√31/2) - (5/2)x = (- √31-5)/2

Question 4 :

Solve the quadratic equation  4 x² + 4 b x - (a² - b²) = 0  by completing the square method

Solution:

4 x² + 4 b x - (a² - b²) = 0

dividing the whole equation by 4,we get

x² +  b x - (a² - b²)/4= 0 x = (a - b)/2        or  x = (-a -b)/2

Question 5 :

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

Solution:

x² - ( √3 + 1) x + 3 = 0  x = -1 , -3

We hope that the students would have understood the stuff and example problems explained on "Complete the square worksheet".

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