Solve the following quadratic equations by the method of completing the square:

4x² + 4bx – (a² – b²) = 0

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

Now the 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

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

(x ± A)² = k²

Taking Square root of both sides.

Now taking the positive part,

x = (a – b) / 2

Now taking the negative part,

x = - (a + b) / 2