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$Rewrite the equation by completing the square. {:[x^(2)+6x+9=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+6x+9=0$ , $(x+\square)^2=\square$

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Solve a quadratic equation by completing the square

Full solution

Q. Rewrite the equation by completing the square.

\newline

x^2+6x+9=0

,

(x+\square)^2=\square

Identify the equation: Identify the equation to be rewritten by completing the square. $\newline$ We have the equation $x^2 + 6x + 9 = 0$ .
Recognize perfect square trinomial: Recognize that the equation is already a perfect square trinomial. $\newline$ The equation $x^2 + 6x + 9$ is a perfect square because it can be factored into $(x + 3)^2$ . The term $9$ is the square of $3$ , and $6x$ is twice the product of $x$ and $3$ .
Rewrite in completed square form: Rewrite the equation in completed square form. $\newline$ Since $x^2 + 6x + 9$ is a perfect square trinomial, it can be written as $(x + 3)^2 = 0$ .

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