Here,
x^2+5x-6=0x2+5x−6=0
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To complete perfect square let MM be the third term,
such that x^2+5x +M x2+5x+M is a perfect square.
So,
color(blue)((i)1^(st) term=x^2(i)1stterm=x2
color(blue)((ii)2^(nd)term=5x(ii)2ndterm=5x
color(blue)((iii)3^(rd)term=M(iii)3rdterm=M
Formula :
color(blue)(3^(rd)term=(2^(nd)term)^2/(4xx 1^(st) term)3rdterm=(2ndterm)24×1stterm
M=(5x)^2/(4xxx^2)=(25x^2)/(4x^2)=25/4M=(5x)24×x2=25x24x2=254
i.e. x^2+5x+(25/4) i.e.x2+5x+(254) is a perfect square.
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So,
x^2+5x=6x2+5x=6
=>x^2+5x+color(red)(25/4)=6+color(red)(25/4⇒x2+5x+254=6+254
=>(x+5/2)^2=(49)/4=(7/2)^2⇒(x+52)2=494=(72)2
=>x+5/2=+-7/2⇒x+52=±72
=>x+5/2=7/2 or x+5/2=-7/2⇒x+52=72orx+52=−72
=>x=7/2-5/2 or x=-7/2-5/2⇒x=72−52orx=−72−52
=>x=2/2 or x=-12/2⇒x=22orx=−122
=>x=1 or x=-6⇒x=1orx=−6
