Question

1. solve the quadratic equation. $-3x^{2}+9x - 1 = 0$ 1) write one exact solution in each box. you can add or remove boxes. if there are no real solutions, remove all boxes.

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, here $a=-3$, $b=9$, $c=-1$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Step3: Calculate discriminant

$$b^2-4ac=9^2-4(-3)(-1)=81-12=69$$

Step4: Substitute into formula

$$x=\frac{-9\pm\sqrt{69}}{2(-3)}=\frac{-9\pm\sqrt{69}}{-6}=\frac{9\mp\sqrt{69}}{6}$$

Step5: Simplify solutions

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

Answer:

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