Given the quadratic equation:
[tex]x^2+5x-5=0[/tex]
Using the general solution for quadratic equations:
[tex]ax^2+bx+c=0\Rightarrow x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
From the problem, we identify:
[tex]\begin{gathered} a=1 \\ b=5 \\ c=-5 \end{gathered}[/tex]
Then:
[tex]x=\frac{-5\pm\sqrt{25+20}}{2}=\frac{-5\pm3\sqrt{5}}{2}[/tex]
And the solution set is:
[tex]\lbrack\frac{-5-3\sqrt{5}}{2},\frac{-5+3\sqrt{5}}{2}][/tex]
