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$Rewrite the equation by completing the square. {:[x^(2)+16 x+64=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+16x+64=0$ $\newline$ $(x+\square)^2=\square$

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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+16x+64=0

\newline

(x+\square)^2=\square

Given quadratic equation: We start with the given quadratic equation. $\newline$ $x^2 + 16x + 64 = 0$ $\newline$ We want to rewrite this equation in the form of $(x + a)^2 = b$ .
Completing the square: First, we identify the coefficient of $x$ , which is $16$ . To complete the square, we need to find $(\frac{16}{2})^2$ . $\newline$ $(\frac{16}{2})^2 = 8^2 = 64$
Perfect square trinomial: We notice that the constant term in the equation, $64$ , is already equal to $(\frac{16}{2})^2$ . This means the equation is already a perfect square trinomial. $\newline$ $x^2 + 16x + 64 = (x + 8)^2$
Rewriting in completed square form: Now we rewrite the equation in the completed square form. $\newline$ $(x + 8)^2 = 0$

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