Given the following question:
[tex]\begin{gathered} x^2+3x-5=0 \\ \text{ Convert using the quadratic formula:} \\ x^2+3x-5=0=x_{1,\:2}=\frac{-3\pm\sqrt{3^2-4\cdot\:1\cdot\left(-5\right)}}{2\cdot\:1} \\ x_{1,\:2}=\frac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \left(-5\right)}}{2\cdot \:1} \\ \text{ Solve} \\ 3^{2}-4\times1(-5) \\ 1\times-5=-5 \\ 3^2-4\times-5 \\ 3^2=3\times3=9 \\ =29 \\ =\sqrt{29} \\ x_{1,\:2}=\frac{-3\pm \sqrt{29}}{2\cdot \:1} \\ \text{ Seperate the solutions:} \\ x_1=\frac{-3+\sqrt{29}}{2\cdot \:1} \\ x_2=\frac{-3-\sqrt{29}}{2\cdot\:1} \\ \text{ Simplify} \\ 2\times1=2 \\ x=\frac{-3+\sqrt{29}}{2} \\ x=\frac{-3-\sqrt{29}}{2} \end{gathered}[/tex]
Your answers are the first and second options.
