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$Rewrite the equation by completing the square. {:[x^(2)+2x-8=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+2x-8=0$ $\newline$ $(x+\square)^2=\square$

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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+2x-8=0

\newline

(x+\square)^2=\square

Rewrite equation in standard form: Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ We start with the equation $x^2 + 2x - 8 = 0$ and add $8$ to both sides to isolate the $x^2$ and $x$ terms on one side. $\newline$ $x^2 + 2x - 8 + 8 = 0 + 8$ $\newline$ $x^2 + 2x = 8$
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 $x$ . In this case, $b = 2$ . $\newline$ $(\frac{2}{2})^2 = 1^2 = 1$ $\newline$ Add $1$ to both sides of the equation. $\newline$ $x^2 + 2x + 1 = 8 + 1$ $\newline$ $x^2 + 2x + 1 = 9$
Factor the left side: 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 $(x + 1)^2$ . $\newline$ $(x + 1)^2 = 9$
Write completed square form: Write the completed square form of the equation. $\newline$ The completed square form of the equation is $(x + 1)^2 = 9$ .

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Solve by completing the square.

\newline

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