已知向量$\boldsymbol{a}=\left(4,−2\right)$，$\boldsymbol{b}=\left(1,x\right)$.
(1)若$\boldsymbol{a}⊥\left(2\boldsymbol{a}+\boldsymbol{b}\right)$，求$x$的值；
(2)若$m\boldsymbol{a}+4\boldsymbol{b}=\left(8,−10\right)$，求向量$\boldsymbol{a}$与$\boldsymbol{b}$夹角的余弦值.