Answer
Choice B
Work Step by Step
In the form $x^2+bx=c,$ the given equation, $
x^2+12x+5=3
,$ is equivalent to
\begin{align*}\require{cancel}
x^2+12x+5-5&=3-5
\\
x^2+12x&=-2
.\end{align*}
To complete the square of the expression on the left, add $\left( \dfrac{b}{2} \right)^2$ on both sides. That is
\begin{align*}\require{cancel}
x^2+12x+\left( \dfrac{12}{2} \right)^2&=-2+\left( \dfrac{12}{2} \right)^2
\\\\
x^2+12x+\left( 6 \right)^2&=-2+\left( 6 \right)^2
\\
x^2+12x+36&=-2+36
\\
x^2+12x+36&=34
.\end{align*}
The expression above is a perfect square trinomial since it takes the form $x^2+2ax+a^2.$ Its factored form is $(x+a)^2.$ Therefore, the equation above is equivalent to
\begin{align*}
(x+6)^2=34
.\end{align*}
Hence, Choice B.
