Question

find the roots of the quadratic equation 4x square +4bx-[a square-b square] =0 by method of completing square.
[answer step by step no need of any thing other then answer] ​

Answer 1

Answer:

Now in the above quadratic equation the coefficient of x² is 4. Let us make it unity by dividing the entire quadratic equation by 4.

4x² + 4bx – (a² – b²) = 0

x² + bx = (a² – b²)/4

Now by taking half of the coefficient of x and then squaring it and adding on both LHS and RHS sides.

Coefficient of x = b

Half of b = b/2

Squaring the half of b = b/4

X²+bx+b²/4=(a²-b²) /4+b²/4

Now LHS term is a perfect square and can be expressed in the form of (a-b)²=a²-2ab+b² where a=x and b=b/2 .

[x+b/2]²=a²-b²+b²/4

[x+b/2]²=a²/4

On simplifying both RHS and LHS we get an equation of the following form.

(x±A)²=k²

[x+b/2]²=a²/4

Taking square root of both sides

[x+b/2]=±a/2

Now taking the positive part

x+b/2=a/2

x=a/2-b/2

x=(a-b) /2

Now taking the negative part .

x+b/2=-a/2

x=-a/2-2-b/2

x=-(a+b) /2.

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