Answer
$x=4.45,-0.45$
Work Step by Step
Consider the expression: $f(x)=-\frac{1}{2}x^2+2x+6$
or, $x^2-4x-12=-10$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-4$
To complete the square, add $4$ on both sides.
$x^2-4x-12+4=-10+4$
$x^2-4x+4=-10+4+12$
$(x-2)^2=6$
$\implies (x-2)=2.45$
and
$(x-2)=-2.45$
or, $x=4.45,-0.45$
