Diagonal forms over quadratic extensions of $\mathbb{Q}_2$

In 1920, Emil Artin conjectured: Let $K$ be a field complete with respect to a discrete absolute value, with finite residue field. Then every homogeneous form with coefficients in $K$ and degree $d$ with at least $d^2+ 1$ variables admits a non-trivial zero. In this article, we prove the conjecture for diagonal forms of degree $d$ not power of 2 over any quadratic extension of $\mathbb{Q}_2$.