Answer
{$\frac{5 - \sqrt {33}}{2},\frac{5 + \sqrt {33}}{2}$}
Work Step by Step
Step 1: Comparing $a^{2}-5a-2=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$, we obtain:
$a=1$, $b=-5$ and $c=-2$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a, b and c in the formula:
$x=\frac{-(-5) \pm \sqrt {(-5)^{2}-4(1)(-2)}}{2(1)}$
Step 4: $x=\frac{5 \pm \sqrt {25+8}}{2}$
Step 5: $x=\frac{5 \pm \sqrt {33}}{2}$
Step 6: $x=\frac{5 + \sqrt {33}}{2}$ or $x=\frac{5 - \sqrt {33}}{2}$
Step 7: Therefore, the solution set is {$\frac{5 - \sqrt {33}}{2},\frac{5 + \sqrt {33}}{2}$}.
