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$Rewrite the equation by completing the square. {:[x^(2)-4x+3=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2-4x+3=0$ $\newline$ $(x+\square)^2=\square$

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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+3=0

\newline

(x+\square)^2=\square

Move constant term: To complete the square, we need to form a perfect square trinomial on the left side of the equation. We start by moving the constant term to the right side of the equation. $\newline$ $x^2 - 4x + 3 = 0$ $\newline$ $x^2 - 4x = -3$
Find completing number: Next, we find the number that completes the square. This number is $(\frac{b}{2})^2$ , where $b$ is the coefficient of $x$ . In this case, $b = -4$ , so $(\frac{b}{2})^2 = (\frac{-4}{2})^2 = (-2)^2 = 4$ . $\newline$ We add this number to both sides of the equation to maintain equality. $\newline$ $x^2 - 4x + 4 = -3 + 4$
Add completing number: Now, the left side of the equation is a perfect square trinomial, and the right side is the sum of $-3$ and $4$ . $\newline$ $x^2 - 4x + 4 = 1$
Write as square of binomial: We can now write the left side as the square of a binomial. $\newline$ $(x - 2)^2 = 1$ $\newline$ This is the completed square form of the equation.

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