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

Feb 29, 2016

$x = 6 , - 4$

#### Explanation:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

and the general formula of a quadratic equation is:

$a {x}^{2} + b x + c = 0$

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

[Solution]

${x}^{2} - 2 x - 24 = 0$

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

Evaluating the quadratic equation with the values above...

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$x = \frac{- \left(- 2\right) \pm \sqrt{{\left(- 2\right)}^{2} - 4 \left(1\right) \left(- 24\right)}}{2 \left(1\right)}$
$x = \frac{2 \pm \sqrt{4 + 96}}{2}$
$x = \frac{2 \pm \sqrt{100}}{2}$
$x = \frac{2 \pm 10}{2}$
$x = \frac{12}{2} , - \frac{8}{2}$
$x = 6 , - 4$

[Checking -> Using Factorisation]
${x}^{2} - 2 x - 24 = 0$
$\left(x - 6\right) \left(x + 4\right) = 0$
$x = 6 , - 4$

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