Question

use the quadratic formula to solve for x.
$6x^2 - 9x + 1 = 0$
round your answer to the nearest hundredth.
if there is more than one solution, separate them with commas.

Explanation:

Step1: Identify quadratic coefficients

For $6x^2 - 9x + 1 = 0$, we have $a=6$, $b=-9$, $c=1$.

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

Compute $b^2 - 4ac = (-9)^2 - 4(6)(1) = 81 - 24 = 57$.

Step4: Compute two solutions

First solution: $x_1 = \frac{9 + \sqrt{57}}{12}$
$\sqrt{57} \approx 7.55$, so $x_1 \approx \frac{9 + 7.55}{12} = \frac{16.55}{12} \approx 1.38$
Second solution: $x_2 = \frac{9 - \sqrt{57}}{12}$
$x_2 \approx \frac{9 - 7.55}{12} = \frac{1.45}{12} \approx 0.12$

Answer:

1.38, 0.12