Question

solve for x.
\\(45x^{2} + 18x + 1 = 0\\)
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
\\(x = \square\\)
submit

Explanation:

Step1: Identify quadratic coefficients

For $ax^2+bx+c=0$, $a=45$, $b=18$, $c=1$

Step2: Apply quadratic formula

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

Step3: Calculate discriminant

$\sqrt{18^2-4(45)(1)}=\sqrt{324-180}=\sqrt{144}=12$

Step4: Compute solutions

$x=\frac{-18+12}{2(45)}=\frac{-6}{90}=-\frac{1}{15}$
$x=\frac{-18-12}{2(45)}=\frac{-30}{90}=-\frac{1}{3}$

Answer:

$-\frac{1}{15}, -\frac{1}{3}$