$$ \mid \leftarrow \quad $$ Find the value of c such that the expression is a perfect-square trinomial.

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Assume the quadratic expression is  
$$
x^2 + bx + c,
$$
and we want it to be a perfect‑square trinomial. A perfect-square trinomial can be written in the form  
$$
\left(x + d\right)^2 = x^2 + 2dx + d^2.
$$
By comparing coefficients we see that the linear term gives  
$$
2d = b,
$$
so  
$$
d = \frac{b}{2},
$$
and the constant term must equal  
$$
d^2 = \left(\frac{b}{2}\right)^2.
$$
Thus, for the expression to be a perfect-square, we must have  
$$
c=\left(\frac{b}{2}\right)^2.
$$

If you have a specific value for $$ b $$, substitute it to find $$ c $$.
To make the expression $$ x^2 + bx + c $$ a perfect-square trinomial, set $$ c $$ equal to $$ \left(\frac{b}{2}\right)^2 $$.

Find the value of c such that the expression is a perfect-square trinomial.

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