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$Rewrite the equation by completing the square. {:[x^(2)+2x-48=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+2x-48=0$ $\newline$ $(x+\square)^2=\square$

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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-48=0

\newline

(x+\square)^2=\square

Rewrite equation in standard form: Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Add $48$ to both sides to isolate the quadratic and linear terms. $\newline$ $x^2 + 2x - 48 + 48 = 0 + 48$ $\newline$ $x^2 + 2x = 48$
Isolate the quadratic and linear terms: Choose the number to complete the square. $\newline$ Since $(\frac{2}{2})^2 = 1$ , add $1$ to both sides to complete the square. $\newline$ $x^2 + 2x + 1 = 48 + 1$ $\newline$ $x^2 + 2x + 1 = 49$
Complete the square: Factor the left side as a perfect square trinomial. $\newline$ $(x + 1)^2 = 49$
Factor the left side: Write the completed square form of the equation. $\newline$ The completed square form of the equation is $(x + 1)^2 = 49$ .

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