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$Rewrite the equation by completing the square. {:[x^(2)+4x-21=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+4x-21=0$ $\newline$ $(x+\square)^2=\square$

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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+4x-21=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 $x^2 + 4x - 21 = 0$ and add $21$ to both sides to isolate the $x^2$ and $x$ terms on one side. $\newline$ $x^2 + 4x - 21 + 21 = 0 + 21$ $\newline$ $x^2 + 4x = 21$
Isolate $x^2$ and $x$ terms: Find the number to complete the square. $\newline$ To complete the square, we need to add $(b/2)^2$ to both sides of the equation, where $b$ is the coefficient of $x$ . In this case, $b = 4$ . $\newline$ $(4/2)^2 = (2)^2 = 4$ $\newline$ We add $4$ to both sides of the equation. $\newline$ $x^2 + 4x + 4 = 21 + 4$ $\newline$ $x^2 + 4x + 4 = 25$
Find completing the square number: 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 $(x + 2)^2$ . $\newline$ $(x + 2)^2 = 25$
Factor left side of equation: Write the completed square form of the equation. $\newline$ The completed square form of the equation is $(x + 2)^2 = 25$ .

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