Solve: 4x^{2} + 4bx – (a^{2} – b^{2}) = 0.

Using splitting middle term, the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation

And either of their sum or difference = b

=

Thus the two terms are

Difference =

=

=

Product =

=

using

=

using

2x[2x + (a + b)] - (a - b)[2x + (a + b)] = 0

[2x - (a - b)][2x + (a + b)] = 0

[2x - (a - b)] = 0 or [2x + (a + b)] = 0

2x = (a - b) or 2x = - (a + b)

Hence roots of equation are

52