This program is based on the Quadratic Formula x =  -b ±√(b^2 - 4ac)/2a.


The Derivation of Quadratic Formula Using Completing the Square Technique:

The standard form of a quadratic equation.

ax^2 + bx + c = 0

Divide the equation by a (the coefficient of x^2).

x^2 + (b/a)x + (c/a) = 0

Subtract c/a from both sides of this equation.
x^2 + (b/a)x = -c/a

Complete the square by adding (b/2a)^2 to both sides of the equation.
x^2 + (b/a)x + (b/2a)^2 = (-c/a) + (b/2a)^2

Using the identity a^2 + 2ab + b^2 = (a + b)^2,
[x + (b/2a)]^2 = (-c/a) + (b^2/4a^2)

[x + (b/2a)]^2 = (b^2 – 4ac)/4a^2

Take the square root on both sides,
 ±√[x + (b/2a)]^2 =  ±√(b^2 – 4ac)/4a^2

Simplify
x + (b/2a) =  ±√(b^2 - 4ac)/2a

x =  -b ±√(b^2 - 4ac)/2a


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