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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic. $\newline$ $s^2 - 16s + \_\_\_\_$

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Complete the square

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Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

s^2 - 16s + \_\_\_\_

Identify coefficients: Identify the values of $a$ , $b$ , and $c$ in the polynomial $s^2 - 16s + ?$ by comparing it to the standard quadratic form $ax^2 + bx + c$ . $a = 1$ $b = -16$ $c = ?$
Calculate half value: To complete the square, we need to add the square of half of the coefficient of $s$ , which is $\frac{b}{2}$ , to the polynomial. $\newline$ Half of $-16$ is $-\frac{16}{2}$ , which equals $-8$ .
Square half value: Now, square the value obtained in the previous step to find the number that completes the square. $\newline$ $(-8)^2$ equals $64$ .
Complete the square: The number that completes the square is $64$ . So the polynomial becomes a perfect-square quadratic when we add $64$ to it. $\newline$ The completed square form is $s^2 - 16s + 64$ .

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