Question

What is the quadratic formula?

Answer 1

`x=(-b+-sqrt(b^2-4ac))/(2a)`

Explanation:

Negative b plus minus the square root of b squared minus 4*a*c over 2*a. To plug something into the quadratic formula the equation needs to be in standard form (`ax^2 + bx^2 +c`).

hope this helps!

Answer 2

If we have:

`ax^2 + bx + c = 0`

Then:

`x = (- b +-sqrt(b^2-4ac))/(2a)`

Explanation:

The quadratic formula provides a method of solving a generic quadratic equation:

`ax^2 + bx + c = 0`

To solve the equation we first factor out `a`:

`a{x^2 + b/ax + c/a} = 0 => x^2 + b/ax + c/a = 0`

Then we complete the square:

`(x + b/(2a))^2 - (b/(2a))^2 + c/a = 0`

Now, we solve for `x`:

`(x + b/(2a))^2 = (b/(2a))^2 - c/a`
`" " = b^2/(4a^2) - c/a`

`" " = b^2/(4a^2) - (4ac)/(4a^2)`

`" " = (b^2-4ac)/(4a^2)`

By taking square root we get:

`x + b/(2a) = +-sqrt((b^2-4ac)/(4a^2))`

`" " = +-sqrt(b^2-4ac)/(2a)`

So that:

`x = - b/(2a) +-sqrt(b^2-4ac)/(2a)`

`:. x = (- b +-sqrt(b^2-4ac))/(2a)`

Which is known as the "quadratic formula".