2008-07-06, 10:06 PM
Let's see if i can do this right...
ax^2+bx+c=0
x^2 + b/a x = -c/a divide by "a"
x^2 + b/a x + ((1/2)(b/a x))^2 = -c/a + ((1/2)(b/a x))^2 completing the square
x^2 + b/a x + b^2/4a^2 = -c/a + b^2/4a^2 simplified
(x^2 + b/2a )^2 = -c/a + b^2/4a^2 Into binomial form (completed square)
x+ b/2a = sqrt(-c/a + b^2/4a^2 ) square root both sides
x= - b/2a + or - sqrt(-c/a + b^2/4a^2 ) move b/a x to other side
x= - b/2a + or - sqrt((-c/a * 4a/4a) + b^2/4a^2 ) common denominator
x= - b/2a + or - (sqrt( b^2 -4ac))/2a simplified
x= (- b + or - sqrt(b^2 - 4ac))/2a simplify more = quadratic formula.
hopefully you can read this... sorry if it is totally incoherent. but i believe that is how it is done... good luck with this =)
ax^2+bx+c=0
x^2 + b/a x = -c/a divide by "a"
x^2 + b/a x + ((1/2)(b/a x))^2 = -c/a + ((1/2)(b/a x))^2 completing the square
x^2 + b/a x + b^2/4a^2 = -c/a + b^2/4a^2 simplified
(x^2 + b/2a )^2 = -c/a + b^2/4a^2 Into binomial form (completed square)
x+ b/2a = sqrt(-c/a + b^2/4a^2 ) square root both sides
x= - b/2a + or - sqrt(-c/a + b^2/4a^2 ) move b/a x to other side
x= - b/2a + or - sqrt((-c/a * 4a/4a) + b^2/4a^2 ) common denominator
x= - b/2a + or - (sqrt( b^2 -4ac))/2a simplified
x= (- b + or - sqrt(b^2 - 4ac))/2a simplify more = quadratic formula.
hopefully you can read this... sorry if it is totally incoherent. but i believe that is how it is done... good luck with this =)