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$Rewrite the equation by completing the square. {:[x^(2)+16 x+63=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+16x+63=0$ $\newline$ $(x+\square)^2=\square$

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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+63=0

\newline

(x+\square)^2=\square

Rewrite equation in standard form: Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Subtract $63$ from both sides to set the equation up for completing the square. $\newline$ $x^2 + 16x + 63 - 63 = 0 - 63$ $\newline$ $x^2 + 16x = -63$
Add number to complete the square: Find 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 $x$ . $\newline$ In this case, $b = 16$ , so $(\frac{16}{2})^2 = 8^2 = 64$ . $\newline$ Add $64$ to both sides of the equation. $\newline$ $x^2 + 16x + 64 = -63 + 64$
Rewrite equation as perfect square trinomial: Rewrite the equation as a perfect square trinomial. $\newline$ Now that we have added $64$ to both sides, the left side of the equation is a perfect square trinomial. $\newline$ $x^2 + 16x + 64 = 1$ $\newline$ $(x + 8)^2 = 1$

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