# How do you set up the quadratic formula with the correct numbers? x² - 4x - 15 = 0

Jun 7, 2018

$x = \frac{4 + \sqrt{76}}{2} \mathmr{and} \frac{4 - \sqrt{76}}{2}$

#### Explanation:

${x}^{2} - 4 x - 15 = 0$

Recall;

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

Comparing you will have;

$a = 1$

$b = - 4$

$c = - 15$

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

Plugging the values into the equation..

$x = \frac{- \left(- 4\right) \pm \sqrt{{\left(- 4\right)}^{2} - 4 \left(1\right) \left(- 15\right)}}{2 \left(1\right)}$

$x = \frac{4 \pm \sqrt{16 + 60}}{2}$

$x = \frac{4 \pm \sqrt{76}}{2}$

$x = \frac{4 + \sqrt{76}}{2} \mathmr{and} \frac{4 - \sqrt{76}}{2}$

Jun 7, 2018

$\text{see explanation}$

#### Explanation:

$\text{the solution of a quadratic equation in "color(blue)"standard form}$

•color(white)(x)ax^2+bx+c=0;a!=0

$\text{can be solved using the "color(blue)"quadratic formula}$

•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)

${x}^{2} - 4 x - 15 = 0 \text{ is in standard form}$

$\text{with "a=1,b=-4" and } c = - 15$

$x = \frac{- \left(- 4\right) \pm \sqrt{{\left(- 4\right)}^{2} - \left(4 \times 1 \times - 15\right)}}{2 \times 1}$

$\textcolor{w h i t e}{x} = \frac{4 \pm \sqrt{16 + 60}}{2}$

$\textcolor{w h i t e}{x} = \frac{4 \pm \sqrt{76}}{2} = \frac{4 \pm 2 \sqrt{19}}{2} = 2 \pm \sqrt{19}$

$x \approx - 2.36 \text{ or "x~~6.36" to 2 dec. places}$