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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

Given quadratic equation: Start with the given quadratic equation. $\newline$ $x^2 - 16x + 63 = 0$ $\newline$ We want to rewrite this equation by completing the square.
Move constant term: Move the constant term to the right side of the equation. $x^2 - 16x = -63$
Complete the square: Find the number that completes the square. To do this, take half of the coefficient of $x$ , square it, and add it to both sides of the equation. $\newline$ The coefficient of $x$ is $-16$ , so half of $-16$ is $-8$ , and $(-8)^2 = 64$ . $\newline$ $x^2 - 16x + 64 = -63 + 64$
Simplify right side: Simplify the right side of the equation. $x^2 - 16x + 64 = 1$
Write as perfect square: Write the left side of the equation as a perfect square. $\newline$ $(x - 8)^2 = 1$
Equation in completed square form: Now we have the equation in the completed square form. $\newline$ $(x - 8)^2 = 1$

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