Answer
The solution set is $\left\{\frac{1}{4}\right\}$.
Work Step by Step
RECALL:
A quadratic equation of the form $ax^2+bx+c=0$ can be solved using the quadratic formula
$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
The given quadratic equation has:
$a=16
\\b=-8
\\c=1$
Substitute these values into the quadratic formula to obtain:
$x=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(16)(1)}}{2(16)}
\\x=\dfrac{8 \pm \sqrt{64-64}}{32}
\\x=\dfrac{8\pm \sqrt{0}}{32}
\\x =\dfrac{8}{32}
\\x=\dfrac{1}{4}$
Therefore, the solution set is $\left\{\frac{1}{4}\right\}$.
