Question

create a perfect square trinomial in order to solve:
x²+3x+1=0

Answer 1

You must complete the square.
\[x^2+2\frac{3}{2}x+\left(\sqrt{\frac{3}{2}}\right)^2+1-\left(\sqrt{\frac{3}{2}}\right)^2=0\]
\[\left(x+\sqrt{\frac{3}{2}}\right)^2-1/3=0\]
And solve.

Answer 2

ah okay thanks, got it!

Answer 3

Um, it is incorrect. The correct form should be,
\[x^2+2\frac{3}{2}x+\frac{9}{4}+1-\frac{9}{4}=0\\
\left(x+\frac{3}{2}\right)^2-5/4=0\Rightarrow x+3/2=\pm\sqrt{5}/2\Rightarrow\]
\[x=-\frac{3}{2}\pm\frac{\sqrt{5}}{2}\]