Solution
- The solution steps are given below:
[tex]\begin{gathered} \text{ Given the quadratic equation:} \\ ax^2+bx+c=0 \\ \text{ The qudartic formula for finding the variable }x\text{ is:} \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \text{ Thus, we can solve the question given to us using the above formula} \\ x^2+4x=-5 \\ \text{ Rewrite the equation} \\ x^2+4x+5=0 \\ \therefore a=1,b=4,c=5 \\ \\ x=\frac{-4\pm\sqrt{4^2-4(1)(5)}}{2(1)} \\ \\ x=\frac{-4\pm\sqrt{16-20}}{2} \\ \\ x=\frac{-4\pm\sqrt{-4}}{2}=\frac{-4\pm\sqrt{4\times-1}}{2} \\ \\ \text{ By the law of surds we have that:} \\ \sqrt{4\times-1}=\sqrt{4}\times\sqrt{-1} \\ \\ x=\frac{-4\pm(\sqrt{4}\times\sqrt{-1})}{2} \\ \\ x=\frac{-4\pm(2\times\sqrt{-1})}{2} \\ \\ x=-\frac{4}{2}\pm\frac{2\sqrt{-1}}{2} \\ \\ x=-2\pm\sqrt{-1} \\ \\ \text{ But we know that }\sqrt{-1}=i \\ \\ \therefore x=-2\pm i \end{gathered}[/tex]
Final Answer
[tex]x=-2\pm i[/tex]
