Expert: Bobby Soltani - 9/9/2005

Question
prove the formula:
X = -b+-(b^2-4ac)1/2 /2a
by quadratic formula:
in ax^2 + bx + c = 0


1/2=root


Answer
Hi Ahmed,

There are several ways to prove the quadratic method.  Here is the "completing the square" version.

ax^2 +bx + c = 0
ax^2 + bx = -c
x^2 + (bx / a) = -c/a
x^2 + (bx / a) + (b / 2a)^2 = -c / a + (b / 2a)^2
(x + (b / 2a))^2 = -4ac / 4a^2 + (b^2 / 4a^2)
x + (b / 2a)^2 = (b^2 - 4ac) / 4a^2
x + (b / 2a) = +/- sqrt ((b^2 - 4ac) / 4a^2)
x = -b / 2a +/- sqrt(b^2 - 4ac) / 2a
x = (-b +/- sqrt(b^2 - 4ac)) / 2a

Let me know if you have any questions.

Bobby