Question

can someone please explain what a quadratic formula is and how to solve equations using it

Answer 1

The quadratic formula is a general solution for all equations of the form \(ax^2+bx+c=0\). This means that it is an expression for \(x\) in terms of \(a,b,\text{and } c\)...essentially it tells you how to solve any quadratic equation.

Answer 2

Its definition is\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
So suppose you wanted to solve \(2x^2-5x-6\) using the quadratic formula. Then you would simply plug in \(a=2\), \(b=-5\), and \(c=-6\) and out would come your answer.

Answer 3

ok so would that work in a equation like 9n^2 =4+7n

Answer 4

Yep. You just need to get it into the form \(an^2+bn+c=0\)...so you would have \(9n^2-7n-4=0\), and then you can plug it in.

Answer 5

i still dont quite get it what are you plugging in

Answer 6

You are letting \(a=9\), \(b=-7\), and \(c=-4\) (the coefficients), and then you are taking \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
and replacing every \(a\) with 9, every \(b\) with -7, every \(c\) with -4, and then evaluation, which will give you \(x\), which will be your answers (note the \(\pm\)).

Answer 7

wait what happens to the n's

Answer 8

You're solving for n.

Answer 9

ok thanks