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$Rewrite the equation by completing the square. {:[x^(2)+8x+12=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $\begin{array}{l} x^{2}+8 x+12=0 \\ (x+\square)^{2}=\square \end{array}$

Full solution

Q. Rewrite the equation by completing the square.

\newline

\begin{array}{l} x^{2}+8 x+12=0 \\ (x+\square)^{2}=\square \end{array}

Given equation: Start with the given equation. $x^2 + 8x + 12 = 0$ We want to rewrite this equation by completing the square.
Move constant term: Move the constant term to the other side of the equation. $\newline$ $x^2 + 8x = -12$ $\newline$ Now we have the equation in the form $x^2 + bx = c$ .
Find completing number: Find the number that completes the square. $\newline$ To complete the square, we need to add $(\frac{b}{2})^2$ to both sides of the equation. Here, $b = 8$ , so $(\frac{8}{2})^2 = 4^2 = 16$ .
Add completing number: Add $16$ to both sides of the equation. $\newline$ $x^2 + 8x + 16 = -12 + 16$ $\newline$ $x^2 + 8x + 16 = 4$ $\newline$ Now the left side of the equation is a perfect square trinomial.
Factor left side: Factor the left side of the equation. $\newline$ $(x + 4)^2 = 4$ $\newline$ The equation is now written in the form of a completed square.
Check final equation: Check the final equation. $\newline$ We have the equation $(x + 4)^2 = 4$ , which is the original equation rewritten by completing the square.