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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 want to rewrite it by completing the square. $\newline$ First, we need to move the constant term to the other side of the equation by adding $35$ to both sides. $\newline$ $x^2 - 2x = 35$
Find completing square number: Next, we need to find a number to add to both sides of the equation to complete the square. This number is found by taking half of the coefficient of $x$ , which is $-2$ , squaring it, and adding it to both sides. $\newline$ $\left(\frac{-2}{2}\right)^2 = (-1)^2 = 1$ $\newline$ So we add $1$ to both sides of the equation. $\newline$ $x^2 - 2x + 1 = 35 + 1$
Rewrite as perfect square trinomial: Now, we can rewrite the left side of the equation as a perfect square trinomial. $\newline$ $(x - 1)^2 = 36$
Completed square form: The equation is now in the completed square form.

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