Question

Find the roots of x^2 -10 x + 9 = 0 by completing square method.

Answer 1

x^2 - 10x +9 = 0

=> x^2 - 10x = - 9

=> x^2 - 10x + (5)^2 = - 9 + (5)^2

=> (x-5)^2 = - 9 + 25

=> (x-5)^2 = 16

=> (x-5) = plus minus 4.

=> x = 5 plus minus 4

Roots are 5+4 = 9

And 5-4 = 1


Steps to complete a perfect square are as follows :-


Step 1 :- Transfer the constant term in RHS

Step 2 :- Divide the whole equation by the coficient of x^2

Step 3:- Add the square of half of the coficient of x in both sides


Now you will get a perfect square....

Answer 2

HEYA!!

Here is your answer :

Given,

${x}^{2} - 10x + 9 = 0 \\ \\ {x }^{2} - 10x = - 9 \\ \\ add \: {5}^{2} on \: both \: sides \\ \\ {x}^{2} - 2x(5) + {5}^{2} = - 9 + {5}^{2} \\ \\ ( x - 5)^{2} = - 9 + 25 \\ \\ ({x - 5})^{2} = 16 \\ \\ x - 5 = + \: and - \sqrt{16} \\ \\ x - 5 = + \: and - 4 \\ \\ x - 5 = \: 4 \: \: \: \: \: \: x - 5 = - 4 \\ \\ x = 4 + 5 \: \: \: \: x = - 4 + 5 \\ \\ x = 9 \: \: \: x = 1$

Therefore, the roots are 9 and 1..
STEPS FOR THE COMPLETING SQUARE METHOD :

☆ Transfer the single term to RHS.

☆ Divide the whole equation be x^2.

☆ Add the half of the square coefficient on the both sides..

HOPE THIS HELPS U. .