use the quotient property of square roots to derive the quad

use the quotient property of square roots to derive the quadratic formula by solving the quadratic equation ax2 + bx+c=0. Hint : begin by completing the square. I need the answer step by step

Solution

ax2 + bx+c=0

Divide the equation by a:

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

add the term we just found, b²/(4a²), to both sides of the equation:

x^2 +(b/a)x +c/a +b^2/4a^2 = b^2/4a^2

This will give us our perfect square trinomial on the left

(x +b/2a)^2 = b^2/4a^2 - c/a

= (b^2 - 4a*c)/4a^2

Taking square root of both sides:

x+ b/2a = +/- sqrt(b^2 -4ac)/2a

( we put a plus or minus sign in front of the square root to account for both possibilities)

subtract b/a from both sides:

x + b/a -b/a = -b/a +/- sqrt(b^2 -4ac)/2a

x = -b/2a + /- sqrt(b^2 -4ac)/2a

x = { -b + / sqrt( b^2 - 4ac) }/2a