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
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