Question

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

Explanation:

Step1: Calculate discriminant

$\sqrt{b^2-4ac} = \sqrt{25 - (-4)} = \sqrt{29}$

Step2: Substitute into quadratic formula

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} = \frac{5 \pm \sqrt{29}}{2}$

Answer:

$x = \frac{5 \pm \sqrt{29}}{2}$