Question Solve \( 5 a^{2}+10 a=-205 \) by completing the square. (Use a comma to separate multiple values.)

Solve the equation \( 5a^{2}+10a=-205 \). Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(5a^{2}+10a=-205\) - step1: Move the expression to the left side: \(5a^{2}+10a+205=0\) - step2: Solve using the quadratic formula: \(a=\frac{-10\pm \sqrt{10^{2}-4\times 5\times 205}}{2\times 5}\) - step3: Simplify the expression: \(a=\frac{-10\pm \sqrt{10^{2}-4\times 5\times 205}}{10}\) - step4: Simplify the expression: \(a=\frac{-10\pm \sqrt{-4000}}{10}\) - step5: Simplify the expression: \(a=\frac{-10\pm 20\sqrt{10}\times i}{10}\) - step6: Separate into possible cases: \(\begin{align}&a=\frac{-10+20\sqrt{10}\times i}{10}\\&a=\frac{-10-20\sqrt{10}\times i}{10}\end{align}\) - step7: Simplify the expression: \(\begin{align}&a=-1+2\sqrt{10}\times i\\&a=\frac{-10-20\sqrt{10}\times i}{10}\end{align}\) - step8: Simplify the expression: \(\begin{align}&a=-1+2\sqrt{10}\times i\\&a=-1-2\sqrt{10}\times i\end{align}\) - step9: Rewrite: \(a_{1}=-1-2\sqrt{10}\times i,a_{2}=-1+2\sqrt{10}\times i\) - step10: Remove the complex number(s): \(\textrm{No real solution}\) The equation \(5a^{2}+10a=-205\) has no real solutions when solved by completing the square.