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$Rewrite the equation by completing the square. {:[x^(2)-8x+7=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2-8x+7=0$ $\newline$ $(x+\square)^2=\square$

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Solve a quadratic equation by completing the square

Full solution

Q. Rewrite the equation by completing the square.

\newline

x^2-8x+7=0

\newline

(x+\square)^2=\square

Given equation: Start with the given equation $x^2 - 8x + 7 = 0$ . $\newline$ To complete the square, we need to form a perfect square trinomial on the left side of the equation.
Isolating the quadratic and linear terms: Subtract $7$ from both sides to isolate the quadratic and linear terms. $\newline$ $x^2 - 8x + 7 - 7 = 0 - 7$ $\newline$ $x^2 - 8x = -7$
Completing the square: To complete the square, we need to add $(\frac{b}{2})^2$ to both sides, where $b$ is the coefficient of $x$ . In this case, $b = -8$ . $\left(-\frac{8}{2}\right)^2 = (-4)^2 = 16$ Add $16$ to both sides of the equation. $x^2 - 8x + 16 = -7 + 16$
Perfect square trinomial: Now the left side of the equation is a perfect square trinomial. $\newline$ $x^2 - 8x + 16 = 9$ $\newline$ The left side can be factored into $(x - 4)^2$ . $\newline$ $(x - 4)^2 = 9$
Rewriting the equation: We have now rewritten the original equation by completing the square. $\newline$ The completed square form is $(x - 4)^2 = 9$ .

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