Question

Solve the equations by completing the square
(i) x² − 10x + 9 = 0 (ii) x² − 5x + 5= 0 (iii) x² + 7x − 6 = 0

Answer 1

Here is your solution

Answer 2

Solution:

i ) x² - 10x + 9 = 0

=> x² - 10x = -9

=> x² - 2.x.5 = -9

=> x² - 2.x.5 + 5² = 5² - 9

=> ( x - 5 )² = 16

=> x - 5 = ± √16

=> x - 5 = ± 4

=> x = 5 ± 4

=> x = 5 + 4 or x = 5 - 4

x = 9 or x = 1

ii ) x² - 5x + 5 = 0

=> x² - 5x = -5

=> x² - 2.x.(5/2) = -5

=> x² - 2.x.(5/2) + (5/2)² = (5/2)² - 5

=> ( x - 5/2 )² = 25/4 - 5/1

=> ( x - 5/2 )² = ( 25 - 20 )/4

=> ( x - 5/2 )² = 5/4

=> x - 5/2 = ± √(5/4)

=> x - 5/2 = ± √5/2

=> x = 5/2 ± √5/2

=> x = ( 5 ± √5 )/2

Therefore,

x = ( 5 + √5 )/2 or x = ( 5 - √5 )/2

iii ) x² + 7x - 6 = 0

=> x² + 7x = 6

=> x² + 2.x.(7/2) = 6

=> x² + 2.x.(7/2)+(7/2)² = (7/2)² + 6

=> ( x + 7/2 )² = 49/4 + 6/1

=> ( x + 7/2 )² = ( 49 + 24 )/4

=> ( x + 7/2 )² = 73/4

=> x + 7/2 = ± √(73/4 )

=> x = -7/2 ± √73/2

=> x = ( -7 ± √73 )/2

Therefore ,

x = ( -7+√73)/2 or x = ( -7-√73)/2

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