Given the quadratic equation
[tex]x^2+2x+37=0[/tex]
We can find the solution using the quadratic formula. The formula for the method is given below.
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
To get a,b,c we would compare the given equation with the general representation of a quadratic equation
[tex]ax^2+bx+c[/tex]
Therefore, a=1, b=2 and c=37
Thus;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-(4\times1\times37)}}{2\times1} \\ x=\frac{-2\pm\sqrt[]{4-148}}{2} \\ x=\frac{-2\pm\sqrt[]{-144}}{2} \\ \therefore i^2=-1 \\ We\text{ would have;} \\ x=\frac{-2\pm\sqrt[]{144i^2}}{2} \\ x=\frac{-2\pm12i}{2} \\ x=\frac{2(-1\pm6i)}{2} \\ x=-1\pm6i \end{gathered}[/tex]
Answer:
[tex]x=-1\pm6i[/tex]
