26. Find the largest real number $x$ such that
$$
\frac{x^{2}+x-1+\left|x^{2}-(x-1)\right|}{2}=35 x-250 \text {. }
$$
26. Ans: 25
Observe that $\frac{1}{2}(a+b+|a-b|)=\max (a, b)$. Also, $x^{2}>x-1$ since $x^{2}-x+1=$ $\left(x-\frac{1}{2}\right)^{2}+\frac{3}{4}>0$. Thus, we have
$$
\left.\frac{1}{2}\left[x^{2}+x-1+x^{2}-(x-1)\right]\right]=\max \left(x^{2}, x-1\right)=x^{2} .
$$

Thus the equation becomes $x^{2}=35 x-250 \Longrightarrow(x-25)(x-10)=0 \Longrightarrow x=25,10$. Therefore, the largest value of $x$ is 25 .