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 a,b,c values

For $ax^2+bx+c=0$, here $a=6$, $b=-9$, $c=1$

Step2: Write quadratic formula

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

Step3: Substitute values into formula

$$x=\frac{-(-9)\pm\sqrt{(-9)^2-4(6)(1)}}{2(6)}$$

Step4: Calculate discriminant

$\sqrt{81-24}=\sqrt{57}\approx7.55$

Step5: Compute two solutions

First solution: $x=\frac{9+7.55}{12}=\frac{16.55}{12}\approx1.38$
Second solution: $x=\frac{9-7.55}{12}=\frac{1.45}{12}\approx0.12$

Answer:

1.38, 0.12