Question

Did I get number 11 correct? Simplify all irrational and complex situations

Answer 1

Given the quadratic equation

`x^2+2x+37=0`

We can find the solution using the quadratic formula. The formula for the method is given below.

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

To get a,b,c we would compare the given equation with the general representation of a quadratic equation

`ax^2+bx+c`

Therefore, a=1, b=2 and c=37

Thus;

`\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-(4*1*37)}}{2*1} \\ 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=(-2\pm12i)/(2) \\ x=(2(-1\pm6i))/(2) \\ x=-1\pm6i \end{gathered}`

Answer:

`x=-1\pm6i`