How do you get from ax2 bx c to the quadratic formula?

Answer 1

ax2+bx+c=0

Multiply the whole equation by 4a:

4a2x2+4abx+4ac=0

Move the 4ac to the other side:

4a2b2+4abx=-4ac

Add b2 to both sides:

4a2b2+4abx+b2=b2-4ac

The left side of the equation is like (a+b)2=a2+2ab+b2, with a being 2ab and b being b:

(2ax+b)2=b2-4ac

Do a square root on both sides of the equation:

2ax+b=√(b2-4ac)

Move the b to the other side of the equation:

2ax=-b±√(b2-4ac)

Leave only x on the left side of the equation by dividing the right side by 2a:

x=(-b±√(b2-4ac))/2a

The previous explanation:

aX2+bx+c is the same as x=-b (plus or minus the square root) of b2 - 4ac divided by two times a.

x=(-b±√(b^2-4ac))/2a

x can equal (-b+√(b^2-4ac))/2a ∆ (not delta) (-b-√(b^2-4ac))/2a