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$Rewrite the equation by completing the square. {:[x^(2)-14 x+49=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2-14x+49=0$ $\newline$ $(x+\square)^2=\square$

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Solve a quadratic equation by completing the square

Full solution

Q. Rewrite the equation by completing the square.

\newline

x^2-14x+49=0

\newline

(x+\square)^2=\square

Step $1$ : Coefficient of x: The coefficient of x is $-14$ . To complete the square, we need to take half of this coefficient and square it. This will give us the number to add and subtract to complete the square. $\newline$ Half of $-14$ is $-7$ , and squaring $-7$ gives us $49$ . $\newline$ $\left(\frac{-14}{2}\right)^2 = (-7)^2 = 49$
Step $2$ : Completing the square: Now we rewrite the equation $x^2 - 14x + 49 = 0$ by adding and subtracting the number we found, which is $49$ , inside the equation. However, since $49$ is already present as a constant term in the equation, we do not need to add or subtract anything. The equation is already a perfect square. $\newline$ $x^2 - 14x + 49 = (x - 7)^2$
Step $3$ : Rewriting the equation: We can now rewrite the equation as a completed square: $\newline$ $(x - 7)^2 = 0$

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