Question

question
solve the equation for all real solutions in simplest form.
$3n^2 + 17n + 17 = -2$
answer
attempt 1 out of 3
+ additional solution - no solution
$n = $
submit answer

Explanation:

Step1: Rewrite to standard quadratic form

Add 2 to both sides:
$$3n^2 + 17n + 19 = 0$$

Step2: Identify coefficients

For $ax^2+bx+c=0$, $a=3$, $b=17$, $c=19$

Step3: Apply quadratic formula

Quadratic formula: $n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:
$$n=\frac{-17\pm\sqrt{17^2-4(3)(19)}}{2(3)}$$

Step4: Calculate discriminant

$$\sqrt{289-228}=\sqrt{61}$$

Step5: Simplify expression

$$n=\frac{-17\pm\sqrt{61}}{6}$$

Answer:

$n=\frac{-17+\sqrt{61}}{6}$ and $n=\frac{-17-\sqrt{61}}{6}$