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$Rewrite the equation by completing the square. {:[x^(2)-6x-16=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2-6x-16=0$ $\newline$ $(x+\square)^2=\square$

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Solve a quadratic equation by completing the square

Full solution

Q. Rewrite the equation by completing the square.

\newline

x^2-6x-16=0

\newline

(x+\square)^2=\square

Rewrite equation: Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ We start with the equation $x^2 - 6x - 16 = 0$ and add $16$ to both sides to isolate the $x^2$ and $x$ terms on one side. $\newline$ $x^2 - 6x - 16 + 16 = 0 + 16$ $\newline$ $x^2 - 6x = 16$
Isolate $x^2$ and $x$ terms: Choose the number to complete the square. $\newline$ To complete the square, we need to add $(\frac{b}{2})^2$ to both sides of the equation, where $b$ is the coefficient of $x$ . In this case, $b = -6$ . $\newline$ $(\frac{-6}{2})^2 = (-3)^2 = 9$ $\newline$ We add $9$ to both sides of the equation. $\newline$ $x^2 - 6x + 9 = 16 + 9$ $\newline$ $x^2 - 6x + 9 = 25$
Complete the square: Factor the left side of the equation. $\newline$ The left side of the equation is now a perfect square trinomial, which can be factored into $(x - 3)^2$ . $\newline$ $(x - 3)^2 = 25$
Factor left side: Write the completed square form of the equation. $\newline$ The completed square form of the equation is $(x - 3)^2 = 25$ .

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