Find one of the roots of the quadratic equation 2x2−7x+3=0 by the method of completion of the square. Also, what is the equation obtained after completion of the square?
3
2x2−7x+3=0
Dividing by the coefficient of x2, we get
x2−72x+32=0; a=1, b=72, c=32
Adding and subtracting the square of b2=74, (half of coefficient of x)
we get,
[x2−2(74)x+(74)2]−(74)2+32=0
(x−74)2−2516=0
Taking Square root, (x−74)=(±54)
Taking positive sign 54, x=3
Taking negative sign −54, x=12