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$Rewrite the equation by completing the square. {:[x^(2)+2x-35=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+2x-35=0$ $\newline$ $(x+\square)^2=\square$

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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-35=0

\newline

(x+\square)^2=\square

Move constant term: We start with the equation $x^2 + 2x - 35 = 0$ and move the constant term to the right side of the equation. $\newline$ $x^2 + 2x = 35$
Complete the square: 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, $b = 2$ , so $(\frac{b}{2})^2 = (\frac{2}{2})^2 = 1^2 = 1$ . $\newline$ $x^2 + 2x + 1 = 35 + 1$
Factor perfect square trinomial: Now we have the left side of the equation in a perfect square trinomial form, which can be factored into $(x + 1)^2$ . $\newline$ $(x + 1)^2 = 36$
Rewritten equation: We have successfully rewritten the equation by completing the square. $\newline$ The completed square form of the equation is $(x + 1)^2 = 36$ .

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