Solve ax²+bx+c=0 by completing Square 

PurnaBargare Parinat Kari Samadhan Kara
(Sridhar Acharya Method)

ax²+bx+c=0

⇒4a(ax²+bx+c=0) multiply the equation with 4a

⇒4a²x²+4abx+4ac=0

⇒4a²x²+4abx=-4ac

⇒(2ax)²+2.2ax.b+(b)²=-4ac+(b)²

⇒(2ax+b)²=(b)²-4ac

⇒ 2ax+b=±√(b²-4ac)

⇒2ax=-b±√(b²-4ac)

⇒x={-b±√(b²-4ac)}/2a

Hence the two roots are {-b±√(b²-4ac)}/2a

Example: Solve the Quadratic equation by competing square(Purna Bargare Parinat Kari Samadhan Kara)

 (Sridhar Acharya Method) 

    2x²-9x+4=0

    Solution:

    2x²-9x+4=0

⇒4×2(2x²-9x+4)=0multiply the equation with 4a
⇒16x²-72x+32=0
⇒(4x)²-72x=-32
⇒(4x)²-2.4x.9+(9)²=-32+(9)²
⇒(4x-9)²=(9)²-32
 ⇒4x-9=±√49

⇒4x=9±7

⇒x=(9+7)/4
   =16/4
   =4
Or
x=(9-7)/4
   =2/4
   =1/2
Hence the two roots are 4 & 1/2

Solve by completing square