ANSWER
[tex]x=\frac{3}{10}+\frac{\sqrt[]{91}}{10}i;x=\frac{3}{10}-\frac{\sqrt[]{91}}{10}i[/tex]
EXPLANATION
To solve the equation given, we have to apply the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
where a = coefficient of x²
b = coefficient of x
c = constant term
From the equation, we have that:
[tex]a=5;b=-3;c=5[/tex]
Therefore, solving for x, we have:
[tex]\begin{gathered} x=\frac{-(-3)\pm\sqrt[]{(-3)^2-4(5)(5)}}{2(5)} \\ x=\frac{3\pm\sqrt[]{9-100}}{10}=\frac{3\pm\sqrt[]{-91}}{10}=\frac{3+\sqrt[]{-1\cdot91}_{}}{10} \\ \Rightarrow x=\frac{3\pm\sqrt[]{91}i}{10} \\ \Rightarrow x=\frac{3}{10}+\frac{\sqrt[]{91}}{10}i;x=\frac{3}{10}-\frac{\sqrt[]{91}}{10}i \end{gathered}[/tex]
That is the solution to the equation.
