use the quadratic formula to solve for x.\n9x² + 3x - 1 = 0\n(if there is more than one solution, separate…

Explanation:

Step1: Identify coefficients

For the quadratic equation $9x^{2}+3x - 1=0$, we have $a = 9$, $b = 3$, $c=-1$.

Step2: Write quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute coefficients

Substitute $a = 9$, $b = 3$, $c=-1$ into the formula: [ \begin{align*} x&=\frac{-3\pm\sqrt{3^{2}-4\times9\times(-1)}}{2\times9}\ &=\frac{-3\pm\sqrt{9 + 36}}{18}\ &=\frac{-3\pm\sqrt{45}}{18}\ &=\frac{-3\pm3\sqrt{5}}{18}\ &=\frac{-1\pm\sqrt{5}}{6} \end{align*} ]

Answer:

$x=\frac{-1+\sqrt{5}}{6},\frac{-1 - \sqrt{5}}{6}$