Answer
$ x\approx 3.6$ and $x\approx -5.6$
Work Step by Step
The given equation is
$\Rightarrow \frac{1}{2}x^2+x-10=0$
Multiply the equation by $2$.
$\Rightarrow x^2+2x-20=0$
Standard equation.
$\Rightarrow ax^2+bx+c=0$
We have $a=1,b=2$ and $c=-20$
Quadratic formula.
$\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute all the values into the formula.
$\Rightarrow x=\frac{-2\pm\sqrt{(2)^2-4(1)(-20)}}{2(1)}$
Clear the parentheses.
$\Rightarrow x=\frac{-2\pm\sqrt{4+80}}{2}$
Simplify.
$\Rightarrow x=\frac{-2\pm\sqrt{84}}{2}$
Simplify square root.
$\Rightarrow x=\frac{-2\pm2\sqrt{21}}{2}$
$\Rightarrow x=-1\pm\sqrt{21}$
The solutions are.
$\Rightarrow x=-1+\sqrt{21}$ and $x=-1-\sqrt{21}$
Simplify.
$\Rightarrow x\approx 3.6$ and $x\approx -5.6$.
