Question

How do you solve `x^2-2x-24=0` using the quadratic formula?

Answer 1

`x = 6, -4`

Explanation:

The quadratic formula is:

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

and the general formula of a quadratic equation is:

`ax^2 + bx + c = 0`

With our current example, `x^2 - 2x - 24 = 0`, we know that our is already in the standard form hence we do not need to do any manipulations to compute for `x`.

[Solution]

`x^2 - 2x - 24 = 0`

We know that:
`a = 1`
`b = -2`
`c = -24`

Evaluating the quadratic equation with the values above...

`x = (-b +- sqrt(b^2 - 4ac))/(2a)`
`x = (-(-2) +- sqrt((-2)^2 - 4(1)(-24)))/(2(1))`
`x = (2 +- sqrt(4 + 96))/2`
`x = (2 +- sqrt(100))/2`
`x = (2 +- 10)/2`
`x = 12/2 , -8/2`
`x = 6, -4`

[Checking -> Using Factorisation]
`x^2 - 2x - 24 = 0`
`(x - 6)(x + 4) = 0`
`x = 6, -4`

Since we got the same answer for both method, we know that our answer is correct.