solve the quadratic equation.\n-3x² + 9x - 1 = 0\nwrite one exact solution in each box. you can add or…

Explanation:

Step1: Identify coefficients

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

Step2: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: [ \begin{align*} x&=\frac{-9\pm\sqrt{9^{2}-4\times(-3)\times(-1)}}{2\times(-3)}\ &=\frac{-9\pm\sqrt{81 - 12}}{-6}\ &=\frac{-9\pm\sqrt{69}}{-6}\ &=\frac{9\pm\sqrt{69}}{6} \end{align*} ]

Answer:

$x=\frac{9+\sqrt{69}}{6}$, $x=\frac{9 - \sqrt{69}}{6}$