Solve the Quadratic Equation: x²+6x+9=0 Step by Step

Let's solve the given equation:

$x^2+6x+9=0$We can identify that the expression on the left side can be factored using the perfect square trinomial formula:

$(a\pm b)^2=a^2\pm2ab+b^2$Let's do this:

$x^2+6x+9=0 \\ x^2\textcolor{blue}{+6x}+3^2=0 \\ x^2\textcolor{blue}{+2\cdot x\cdot3}+3^2=0 \\ \downarrow\\ (x+3)^2=0$We emphasize that factoring using the mentioned formula was possible only because the middle term in the expression (which is in first power in this case and highlighted in blue in the previous calculation) indeed matched the middle term in the perfect square trinomial formula,

We'll continue and solve the resulting equation, which we'll do using square root extraction on both sides:

$(x+3)^2=0 \hspace{6pt}\text{/}\sqrt{\hspace{4pt}}\\ x+3=0\\ \boxed{x=-3}$Therefore, the correct answer is answer B.