Answer:
-3
-7/3
Step-by-step explanation:
Let u=x+2
We need to now solve 3u^2+4u+1=0 for u.
I'm going to try factoring. 3u (u)=3u^2 and 1(1)=1 so I'm going to try factored form (3u+1)(u+1).
Since 3u(1)+1(u)=4u, we are done.
Since (3u+1)(u+1)=0, then either 3u+1=0 or u+1=0.
Let's solve u+1=0 by subtracting 1 on both sides which obtains for us that u=-1.
Let's solve 3u+1=0 by subtracting 1 and then dividing both sides by 3 which obtains for us u=-1/3.
Since u=x+2, we are down to just solving the following:
x+2=-1 and x+2=-1/3
Both equations require us to subtract 2 on both sides.
The solutions are
x=-1-2=-3 and x=-1/3-2=-7/3
Answer:
Step-by-step explanation:
[tex]\Large \boldsymbol {} Let : t=x+2 \ \ ; \ \ t^2=(x+2)^2\\\\3(x+2)^2+4(x+2)+1 =0 \\\\\\3t^2+4t+1=0 \\\\D=16-12=4 \\\\ t_{1}=\dfrac{-4-2}{6} =-1 \ \ ; \ \ \boxed{x_1=-3 }\\\\\\ t_2=\dfrac{-4+2}{6} =-\dfrac{1}{3} \ \ ; \ \boxed{x_2=-2\frac{1}{3} }[/tex]
