Answer
the solution set is\[\left\{ -\frac{1}{3} \right\}\].
Work Step by Step
The given equation can be written as\[9{{x}^{2}}+6x+1=0\].
Compare the given equation with the equation\[a{{x}^{2}}+bx+c=0\].
Here, \[a=9,\,\,b=6,\text{ and }c=1\].
Now put these values in the quadratic formula: \[x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\]
That is,
\[\begin{align}
& x=\frac{-6\pm \sqrt{{{\left( 6 \right)}^{2}}-4\times 9\times 1}}{2\times 9} \\
& =\frac{-6\pm \sqrt{36-36}}{18} \\
& =\frac{-6\pm \sqrt{0}}{18} \\
& =-\frac{1}{3}
\end{align}\]
Hence, the solution set is\[\left\{ -\frac{1}{3} \right\}\].
