I'm not that experienced in math. In fact, I'm not even in high school. I haven't even really done algebra proper, but I've been messing around with the quadratic formula. I'm not even sure if this should go here in Intermediate Algebra, but it is algebra and is not easy so I put it here.
So, I was trying to derive the quadratic formula using The method of adding b^2, because it's simpler
So I successfully derived it, and then noticed something.
4a^2x^2+4abx+b^2 can be simplified to (2ax+b)^2 or (-2ax-b)^2, since there are 2 answers to square roots either positive or negative.
But with the 2nd simplification, something doesn't work.
(-2ax-b)^2 = b^2-4ac
sqrt
-2ax-b=+or-sqrt(b^2-4ac)
add b
-2ax=b+or-sqrt(b^2-4ac)
/-2a
x=b+or-sqrt(b^2-4ac)/-2a
However, I think is wrong, but, being stupid and bad at math, I can't find my error.
Please help (even though you'll probably find the mistake in 5 seconds).
So, I was trying to derive the quadratic formula using The method of adding b^2, because it's simpler
So I successfully derived it, and then noticed something.
4a^2x^2+4abx+b^2 can be simplified to (2ax+b)^2 or (-2ax-b)^2, since there are 2 answers to square roots either positive or negative.
But with the 2nd simplification, something doesn't work.
(-2ax-b)^2 = b^2-4ac
sqrt
-2ax-b=+or-sqrt(b^2-4ac)
add b
-2ax=b+or-sqrt(b^2-4ac)
/-2a
x=b+or-sqrt(b^2-4ac)/-2a
However, I think is wrong, but, being stupid and bad at math, I can't find my error.
Please help (even though you'll probably find the mistake in 5 seconds).