| 2 x 2 − 5 x − 1 | + 1 < x 2 | 2 x 2 − 5 x − 1 | < x 2 − 1 − x 2 + 1 < 2 x 2 − 5 x − 1 < x 2 − 1 {\displaystyle {\begin{aligned}&|2x^{2}-5x-1|+1<x^{2}\\&|2x^{2}-5x-1|<x^{2}-1\\&-x^{2}+1<2x^{2}-5x-1<x^{2}-1\\\end{aligned}}}
2 x 2 − 5 x − 1 < x 2 − 1 x 2 − 5 x < 0 x ( x − 5 ) < 0 x ( x − 5 ) = 0 0 < x < 5 {\displaystyle {\begin{aligned}&2x^{2}-5x-1<x^{2}-1\\&x^{2}-5x<0\\&x(x-5)<0\\&x(x-5)=0\\&0<x<5\\\end{aligned}}}
2 < x < 5 {\displaystyle {\begin{aligned}2<x<5\end{aligned}}}
