Find the roots of 4xsq.+3x+5=0 by the method of completing the square.

Yes, its right. 2 x (2x) x 3/4 is just an other way of writing 3x. 

You can easily solve any quadratic equation by the method of completing square by writing the coefficient of x as product 2 x A x B, in order to use the identity (a+b)² or (a - b)².

Here note that in order to use identity (a+b)² = a² + 2ab + b², a = 2x. Now, we need to write 3x in such a way that 2 x 2x x b = 3x. So, clearly, b = 3/4

Hence, in order to make use of the identity we should write 3x as 2 x (2x) x 3/4.

 

In the solution done by you (by first dividing by 4), the answer is the same only.

Observe that in earlier method, we had:

(2x+3/4)sq.= -71/16

Divide both sides by 4 ,we get,

(2x+3/4)²/ 2²= -71/64

(x+3/8)² = -71/64, which is the same as what you got.

 

 

In order to solve an equation by completing the square method, it is always advisable to start by making the coefficient of x² as 1.