Katie solved the equation by completing the square. $$ \begin{array}{l}x^{2}+12 x-7=0 \ ext { Which equation shows one of the steps Katie could have taken to complete the square? } \ x^{2}+12 x+36=7 \ x^{2}+12 x+144=7+144 \ x^{2}+12 x+144=7 \ x^{2}+12 x+36=7+36\end{array} $$

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Katie solved the equation by completing the square. $$ \begin{array}{l}x^{2}+12 x-7=0 \ 	ext { Which equation shows one of the steps Katie could have taken to complete the square? } \ x^{2}+12 x+36=7 \ x^{2}+12 x+144=7+144 \ x^{2}+12 x+144=7 \ x^{2}+12 x+36=7+36\end{array} $$

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The correct step is $$ x^{2} + 12x + 36 = 7 + 36 $$. To complete the square for the equation $$x^{2}+12x-7=0$$, Katie would need to add the square of half the coefficient of $$x$$ to both sides of the equation. The coefficient of $$x$$ is 12, so half of that is 6, and the square of 6 is 36. The correct step Katie could have taken is to add 36 to both sides of the equation to make the left side a perfect square trinomial. Here is the correct step: $$ x^{2} + 12x + 36 = 7 + 36 $$ This step is necessary to transform the left side of the equation into a perfect square, which is $$(x + 6)^2$$. The right side of the equation is then adjusted to maintain the balance of the equation. The other options provided do not correctly reflect this step.

Katie solved the equation by completing the square. \( \begin{array}{l}x^{2}+12 x-7=0 \\ \text { Which equation shows one of the steps Katie could have taken to complete the square? } \\ x^{2}+12 x+36=7 \\ x^{2}+12 x+144=7+144 \\ x^{2}+12 x+144=7 \\ x^{2}+12 x+36=7+36\end{array} \)

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Katie solved the equation by completing the square. \( \begin{array}{l}x^{2}+12 x-7=0 \\ \text { Which equation shows one of the steps Katie could have taken to complete the square? } \\ x^{2}+12 x+36=7 \\ x^{2}+12 x+144=7+144 \\ x^{2}+12 x+144=7 \\ x^{2}+12 x+36=7+36\end{array} \)

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