Question

use the quadratic formula to solve for x.
$9x^2 - 5x = 1$
round your answer to the nearest hundredth.
if there is more than one solution, separate them with commas.

Explanation:

Step1: Rewrite to standard quadratic form

$9x^2 - 5x - 1 = 0$

Step2: Identify coefficients a,b,c

$a=9,\ b=-5,\ c=-1$

Step3: Apply quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values:
$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(9)(-1)}}{2(9)}$

Step4: Calculate discriminant

$\sqrt{25 + 36} = \sqrt{61} \approx 7.810$

Step5: Compute two solutions

First solution: $x = \frac{5 + 7.810}{18} = \frac{12.810}{18} \approx 0.71$
Second solution: $x = \frac{5 - 7.810}{18} = \frac{-2.810}{18} \approx -0.16$

Answer:

0.71, -0.16