Solution:
Given the number line;
The inequality;
[tex]x^2+5x-5<0[/tex][tex]\begin{gathered} \text{ complete the square;} \\ \\ x^2+5x-5=(x+\frac{5}{2})^2-\frac{45}{4} \\ \\ (x+\frac{5}{2})^2-\frac{45}{4}<0 \\ \\ (x+\frac{5}{2})^2-\frac{45}{4}+\frac{45}{4}<0+\frac{45}{4} \\ \\ (x+\frac{5}{2})^2<\frac{45}{4} \\ \\ -\sqrt{\frac{45}{4}}\frac{-3\sqrt{5}}{2}-\frac{5}{2} \\ \\ -\sqrt{\frac{45}{4}}\frac{-3\sqrt{5}-5}{2} \end{gathered}[/tex]
Also;
[tex]x+\frac{5}{2}<\sqrt{\frac{45}{4}}:x<\frac{3\sqrt{5}-5}{2}[/tex]
Combine the intervals;
[tex]\frac{-3\sqrt{5}-5}{2}Thus,
the line graph is;
