Answer
The solution to the equation is
[tex]x=-1\pm\frac{i\sqrt[]{2}}{3}[/tex]This can be written as
x = -1 ± 0.4714i
Or even be broken down further into
[tex]\begin{gathered} x=-1+\frac{i\sqrt[]{2}}{3} \\ OR \\ x=-1-\frac{i\sqrt[]{2}}{3} \end{gathered}[/tex]Explanation
The quadratic formula can be used to solve all quadratic equations of the form
ax² + bx + c = 0
The quadratic formula is given as
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]For this question, we can write this given equation in the general form of a quadratic equation
9x² + 18x = -11
9x² + 18x + 11 = 0
Comparing this with ax² + bx + c = 0
a = 9
b = 18
c = 11
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-18\pm\sqrt[]{18^2-4(9)(11)}}{2(9)} \\ x=\frac{-18\pm\sqrt[]{324-396}}{18} \\ x=\frac{-18\pm\sqrt[]{-72}}{18} \end{gathered}[/tex]Noting that the square root of -1 is the complex number i
√(-72) = i√72
But,
√(72) = √(36×2) = √(36) × √(2) = 6√2
[tex]\begin{gathered} x=\frac{-18\pm\sqrt[]{-72}}{18} \\ x=\frac{-18\pm i\sqrt[]{72}}{18} \\ x=\frac{-18\pm6i\sqrt[]{2}}{18} \\ x=\frac{-18}{18}\pm\frac{6i\sqrt[]{2}}{18} \\ x=-1\pm\frac{i\sqrt[]{2}}{3} \\ x=1+\frac{i\sqrt[]{2}}{3} \\ OR \\ x=-1-\frac{i\sqrt[]{2}}{3} \end{gathered}[/tex]Hope this Helps!!!
