Question

quadratic equation solving
$x^2 - 5x - 18 = 0$
identify terms for the quadratic formula, then solve for $x$.
$x^2 - 5x - 18 = 0$
for $ax^2+bx+c=0$
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$a=1$ $b=-5$ $c=-18$
$-b=5$ $4ac=-72$
$b^2=25$ $2a=2$
$x=\pm\sqrt{\quad}$

Explanation:

Step1: Calculate discriminant

$\sqrt{b^2-4ac} = \sqrt{25 - (-72)} = \sqrt{97}$

Step2: Substitute into quadratic formula

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} = \frac{5 \pm \sqrt{97}}{2}$

Step3: Split into two solutions

$x_1 = \frac{5 + \sqrt{97}}{2}$, $x_2 = \frac{5 - \sqrt{97}}{2}$

Answer:

$x = \frac{5 + \sqrt{97}}{2}$ or $x = \frac{5 - \sqrt{97}}{2}$