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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic. $\newline$ $q^2 - 12q + \underline{\hspace{2em}}$

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Complete the square

Full solution

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

\newline

q^2 - 12q + \underline{\hspace{2em}}

Identify coefficients: Identify the values of $a$ , $b$ , and $c$ in the quadratic expression. $\newline$ Leading coefficient ( $a$ ): $1$ $\newline$ Coefficient of linear term ( $b$ ): $-12$ $\newline$ Constant ( $c$ ): $?$
Complete the square: Determine the value needed to complete the square. $\newline$ To complete the square for $q^2 - 12q$ , add $\left(-\frac{12}{2}\right)^2$ . $\newline$ Perfect square quadratic: $q^2 - 12q + \left(-\frac{12}{2}\right)^2$
Calculate missing value: Calculate $(-12/2)^2$ to find the missing value in $q^2 − 12q + \_\_\_$ . $\newline$ $(-12/2)^2$ $\newline$ $= (-6)^2$ $\newline$ $= 36$

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