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Find the roots of 4xsq.+3x+5=0 by the method of completing the square.
Asked by Murali | 06 Oct, 2013, 09:38: PM Expert Answer
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)= -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.
Answered by | 06 Oct, 2013, 10:03: PM

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