Answer:
x = (-1 + √(26)i)/9
x = (-1 - √(26)i)/9
Explanation:
If we have an equation of the form ax² + bx + c = 0, we can solve it using the quadratic equation
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, the given equation is
9x² + 2x = -3
This can be rewritten as
9x² + 2x + 3 = -3 + 3
9x² + 2x + 3 = 0
So, a = 9, b = 2 and c = 3. Therefore, the solutions using the quadratic equation are
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4(9)(3)}}{2(9)} \\ x=\frac{-2\pm\sqrt[]{-104}_{}}{18} \\ x=\frac{-2\pm\sqrt[]{104}i}{18} \\ x=\frac{-2\pm2\sqrt[]{26}i}{18} \\ \text{Then} \\ x=\frac{-2+2\sqrt[]{26}i}{18}=\frac{-1+\sqrt[]{26}i}{9} \\ or \\ x=\frac{-2-2\sqrt[]{26}i}{18}=\frac{-1-\sqrt[]{26}i}{9} \end{gathered}[/tex]therefore, the solutions are
x = (-1 + √(26)i)/9
x = (-1 - √(26)i)/9
