Step1: write out the equation
[tex]x^2+4x-1=0^{}[/tex]Looking at the equation it cannot be factorized, hence we use the quadratic formula method
Step2: write out the quadratic formula
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}[/tex]where a=coefficient ofx²=1
b=coefficient of x=+4
c= constant =-1
Step3: Substitute the values into the formula above
[tex]x=\frac{-4\pm\sqrt[]{4^2-4(1)(-1)}}{2(1)}[/tex][tex]\begin{gathered} x=\frac{-4\pm\sqrt[]{16+4}}{2} \\ =\frac{-4\pm\sqrt[]{20}}{2} \end{gathered}[/tex]Hence, by splitting the denominator we have
[tex]\begin{gathered} x=\frac{-4}{2}\pm\frac{\sqrt[]{20}}{2} \\ =-2\pm\frac{\sqrt[]{4\times5}}{2} \\ =-2\pm\frac{2\sqrt[]{5}}{2} \\ =-2\pm\sqrt[]{5} \end{gathered}[/tex]x=-2±√5
Therefore the right option is c
