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$Rewrite the equation by completing the square. {:[x^(2)+18 x+80=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $\begin{array}{l} x^{2}+18 x+80=0 \\ (x+\square)^{2}=\square \end{array}$

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Q. Rewrite the equation by completing the square.

\newline

\begin{array}{l} x^{2}+18 x+80=0 \\ (x+\square)^{2}=\square \end{array}

Given equation: Start with the given equation $x^2 + 18x + 80 = 0$ . $\newline$ To complete the square, we need to form a perfect square trinomial on the left side of the equation.
Completing the square: To create a perfect square trinomial, we need to find a value that, when added and subtracted to the equation, completes the square for $x^2 + 18x$ . This value is $(\frac{18}{2})^2 = 9^2 = 81$ .
Adding and subtracting $81$ : Add and subtract $81$ inside the equation to complete the square. We add $81$ to create the perfect square trinomial and subtract $81$ to keep the equation balanced. $\newline$ $x^2 + 18x + 81 - 81 + 80 = 0$
Combining like terms: Combine like terms on the left side of the equation. $\newline$ $x^2 + 18x + 81 = 81 - 80$ $\newline$ $x^2 + 18x + 81 = 1$
Rewriting as a perfect square trinomial: Now, the left side of the equation is a perfect square trinomial, and we can rewrite it as the square of a binomial. $\newline$ $(x + 9)^2 = 1$
Completing the square: The equation is now rewritten by completing the square. $x^2 + 18x + 80 = 0$ , $(x + 9)^2 = 1$