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Math·Advanced Math·Nonlinear equations in one variable and systems of equations in two variables

hard

One solution to the given equation can be written as $x=\frac{-8-k\sqrt{2}}{16}$, where $k$ is a constant. What is the value of $k$? $80x^2+80x=-10$

A

$4$

B

$80$

C

$32$

D

$128$