Question

Need some help frrrr

Answer 1

The solution to the equation is

`x=-1\pm\frac{i\sqrt[]{2}}{3}`

This can be written as

x = -1 ± 0.4714i

Or even be broken down further into

`\begin{gathered} x=-1+\frac{i\sqrt[]{2}}{3} \\ OR \\ x=-1-\frac{i\sqrt[]{2}}{3} \end{gathered}`

Step-by-step 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

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

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

`\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}`

Noting that the square root of -1 is the complex number i

√(-72) = i√72

But,

√(72) = √(36×2) = √(36) × √(2) = 6√2

`\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=(-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}`

Hope this Helps!!!