Answer
$\left\{\dfrac{5- \sqrt{29}}{2},\dfrac{5+ \sqrt{29}}{2}\right\}$
Work Step by Step
The equation is in standard form $ax^2+bx+c=0$.
We have $a=1,b=-5$ and $c=-1$.
The discriminant is
$=b^2-4ac$
$=(-5)^2-4(1)(-1)$
$=25+4$
$=29$
Since $29>0$. There are two real solutions.
The quadratic formula is
$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$
Substitute the values of $a, b, c,$ and the discriminant into the quadratic formula to obtain:
$x=\dfrac{-(-5)\pm \sqrt{(29)}}{2(1)}$
Simplify.
$x=\dfrac{5\pm \sqrt{29}}{2}$
The solution set is $\left\{\dfrac{5- \sqrt{29}}{2},\dfrac{5+ \sqrt{29}}{2}\right\}$.
