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$Rewrite the equation by completing the square. {:[x^(2)+10 x+16=0],[(x+◻)^(2)=◻]:}$

Rewrite the equation by completing the square. $\newline$ $x^2+10x+16=0$ $\newline$ $(x+\square)^2=\square$

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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+10x+16=0

\newline

(x+\square)^2=\square

Finding the Perfect Square Number: To complete the square, we need to find a number that, when added to $x^2 + 10x$ , will make it a perfect square trinomial. We will then adjust the equation accordingly. $\newline$ First, we take the coefficient of $x$ , which is $10$ , divide it by $2$ , and square it to find the number to complete the square. $\newline$ $\frac{10}{2}$ ^ $2$ = $5$ ^ $2$ = $25$
Adjusting the Equation: Now we add and subtract this number inside the equation to maintain the equality. $\newline$ $x^2 + 10x + 25 - 25 + 16 = 0$
Rewriting as a Perfect Square Trinomial: We can now rewrite the equation as a perfect square trinomial plus a constant. $\newline$ $(x + 5)^2 - 25 + 16 = 0$
Simplifying the Constant Terms: Next, we simplify the constant terms on the right side of the equation. $\newline$ $(x + 5)^2 - 9 = 0$
Completing the Square: Finally, we have the equation in the completed square form. $\newline$ $(x + 5)^2 = 9$

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