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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic. $\newline$ $m^2 + 28m + \underline{\hspace{3em}}$

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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

m^2 + 28m + \underline{\hspace{3em}}

Identify values: Identify the values of $a$ , $b$ , and $c$ in the quadratic expression. $\newline$ Leading coefficient ( $a$ ): $1$ $\newline$ Coefficient of linear term ( $b$ ): $28$ $\newline$ Constant ( $c$ ): ?
Determine completion: Determine the value needed to complete the square. $\newline$ To complete the square for $m^2 + 28m$ , add $(b/2)^2$ to the expression. $\newline$ Perfect square quadratic: $m^2 + 28m + (28/2)^2$
Calculate missing value: Calculate $(28/2)^2$ to find the missing value in $m^2 + 28m + \_$ . $\$28/2)^2$ $= 14^2$ $= 196$

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