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$Rewrite the equation by completing the square. {:[x^(2)-14 x+33=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2-14x+33=0$ $\newline$ $(x+\square)^2=\square$

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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+33=0

\newline

(x+\square)^2=\square

Rewrite equation: Rewrite the equation in the form of $x^2 + bx = c$ . $\newline$ Subtract $33$ from both sides to set the equation up for completing the square. $\newline$ $x^2 - 14x + 33 - 33 = 0 - 33$ $\newline$ $x^2 - 14x = -33$
Find completing square number: Find the number to complete the square. $\newline$ To complete the square, we need to add $(\frac{b}{2})^2$ to both sides of the equation, where $b$ is the coefficient of $x$ . $\newline$ In this case, $b = -14$ , so $(\frac{b}{2})^2 = (\frac{-14}{2})^2 = (-7)^2 = 49$ .
Add completing square number: Add $49$ to both sides of the equation. $\newline$ $x^2 - 14x + 49 = -33 + 49$ $\newline$ $x^2 - 14x + 49 = 16$
Factor left side: Factor the left side of the equation. $\newline$ The left side of the equation is now a perfect square trinomial. $\newline$ $(x - 7)^2 = 16$
Write completed square form: Write the completed square form of the equation. $\newline$ The equation in completed square form is: $\newline$ $(x - 7)^2 = 16$

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