>>8071981This was the proof that got me interested in math
I used to just know the quadratic formula but I had no Idea where It came from
ax^2 +bx + c = 0
divide by a
x^2 + bx/a + c/a = 0
subtract c/a
x^2 +bx/a = -c/a
add b^2/4a^2 on both sides
x^2 +bx/a + b^2/4a^2 = -c/a + b^2/4a^2
factorize the left
(x+b/2a)^2 = -c/a + b^2/4a^2
multiply -c/a by 4a/4a
(x+b/2a)^2 = -4ac/4a^2 + b^2/4a^2
get a common denominator
(x+b/2a)^2 = (b^2 -4ac)/4a^2
inverse the left hand side by taking the plus or minus square root of the left side
x + b/2a = ±√((b^2 -4ac)/4a^2)
distribute the root to the top and bottom of the fraction
x + b/2a = ±√(b^2 -4ac)/√4a^2
take the root of the denominator
x + b/2a = ±√(b^2 -4ac)/2a
subtract b/2a from both sides
x = -b/2a ±√(b^2 -4ac)/2a
combine the fractions
x = (-b ±√(b^2 -4ac))/2a
