How do you solve x2+5x−6=0 by completing the square?

1 Answer
maganbhai P.
Jul 26, 2018

x=1orx=−6

Explanation:

Here,
x2+5x−6=0
...........................................................................................................................
To complete perfect square let M be the third term,
such that x2+5x+M is a perfect square.

So,

(i)1stterm=x2
(ii)2ndterm=5x
(iii)3rdterm=M

Formula :
3rdterm=(2ndterm)24×1stterm

M=(5x)24×x2=25x24x2=254

i.e.x2+5x+(254) is a perfect square.
......................................................................................................................
So,

x2+5x=6

⇒x2+5x+254=6+254

⇒(x+52)2=494=(72)2

⇒x+52=±72

⇒x+52=72orx+52=−72

⇒x=72−52orx=−72−52

⇒x=22orx=−122

⇒x=1orx=−6

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