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$Rewrite the equation by completing the square. {:[x^(2)+11 x+24=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+11x+24=0$ $\newline$ $(x+\square)^2=\square$

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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+11x+24=0

\newline

(x+\square)^2=\square

Move constant term: $x^2 + 11x + 24 = 0$ $\newline$ First, we need to move the constant term to the right side of the equation to prepare for completing the square. $\newline$ $x^2 + 11x = -24$
Complete the square: $x^2 + 11x = -24$ $\newline$ To complete the square, we need to add the square of half the coefficient of $x$ to both sides of the equation. The coefficient of $x$ is $11$ , so half of $11$ is $5.5$ , and the square of $5.5$ is $30.25$ . $\newline$ $x^2 + 11x + 30.25 = -24 + 30.25$
Simplify right side: $x^2 + 11x + 30.25 = -24 + 30.25$ $\newline$ Now, we simplify the right side of the equation by adding $-24$ and $30.25$ . $\newline$ $x^2 + 11x + 30.25 = 6.25$
Write as perfect square trinomial: $x^2 + 11x + 30.25 = 6.25$ $\newline$ The left side of the equation is now a perfect square trinomial, and can be written as $(x + 5.5)^2$ . $\newline$ $(x + 5.5)^2 = 6.25$

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