Find the value of c such that the expression is a​ perfect-square trinomial.xsquaredplus4xpluscQuestion content area bottomPart 1cequalsenter your response here​(Simplify your answer. Type an integer or a​ fraction.)

1 answer

To find the value of \( c \) such that the expression \( x^2 + 4x + c \) is a perfect-square trinomial, we can use the formula for a perfect square trinomial, which states:

\[ (x + a)^2 = x^2 + 2ax + a^2 \]

Here, \( 2a \) corresponds to the coefficient of \( x \). In our expression \( x^2 + 4x + c \), the coefficient of \( x \) is 4, so we set:

\[ 2a = 4 \]

Solving for \( a \):

\[ a = \frac{4}{2} = 2 \]

Now, to find \( c \), we substitute \( a \) into the expression \( a^2 \):

\[ c = a^2 = 2^2 = 4 \]

Thus, the value of \( c \) is:

\[ \boxed{4} \]