Answer
$\left\{\dfrac{-\sqrt{2}- \sqrt{10}}{2},\dfrac{-\sqrt{2}+ \sqrt{10}}{2}\right\}$.
Work Step by Step
The equation is in standard form $ax^2+bx+c=0$.
We have $a=1,b=\sqrt{2}$ and $c=-2$.
The discriminant is
$=b^2-4ac$
$=(\sqrt{2})^2-4(1)(-2)$
$=2+8$
$=10$
Since $10>0$. 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 to obtain:.
$x=\dfrac{-(\sqrt{2})\pm \sqrt{(10)}}{2(1)}$
Simplify.
$x=\dfrac{-\sqrt{2}\pm \sqrt{10}}{2}$
Hence, the solution set is $\left\{\dfrac{-\sqrt{2}- \sqrt{10}}{2},\dfrac{-\sqrt{2}+ \sqrt{10}}{2}\right\}$.
