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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic. $\newline$ $x^2 + 20x + \underline{\hspace{1cm}}$

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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

x^2 + 20x + \underline{\hspace{1cm}}

Identify Values: Identify the values of $a$ , $b$ , and $c$ in the quadratic expression. $\newline$ Leading coefficient ( $a$ ): $1$ $\newline$ Coefficient of linear term ( $b$ ): $20$ $\newline$ Constant ( $c$ ): ?
Determine Completion: Determine the value needed to complete the square. $\newline$ To complete the square for $x^2 + 20x$ , add $(b/2)^2$ . $\newline$ Perfect square quadratic: $x^2 + 20x + (20/2)^2$
Calculate Missing Value: Calculate $(20/2)^2$ to find the missing value in $x^2 + 20x + \underline{\hspace{1em}}$ . $\$20/2)^2$ $= 10^2$ $= 100$ The missing value is $100$ .

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