Simplify \(\frac{2}{3}x\) to \(\frac{2x}{3}\).
Factor with quadratic formula.
In general, given \(a{x}^{2}+bx+c\), the factored form is:
\[a(x-\frac{-b+\sqrt{{b}^{2}-4ac}}{2a})(x-\frac{-b-\sqrt{{b}^{2}-4ac}}{2a})\]
In this case, \(a=1\), \(b=\frac{2}{3}\) and \(c=\frac{1}{9}\).
\[(x-\frac{-\frac{2}{3}+\sqrt{{(\frac{2}{3})}^{2}-4\times \frac{1}{9}}}{2})(x-\frac{-\frac{2}{3}-\sqrt{{(\frac{2}{3})}^{2}-4\times \frac{1}{9}}}{2})\]
Simplify.
\[(x+\frac{1}{3})(x+\frac{1}{3})\]
Solve for \(x\).
Ask: When will \((x+\frac{1}{3})(x+\frac{1}{3})\) equal zero?
When \(x+\frac{1}{3}=0\) or \(x+\frac{1}{3}=0\)
Solve each of the 2 equations above.
\[x=-\frac{1}{3}\]
