Determine what c -value will create a perfect square trinomial for the following expression: \( x^{2}+18 x+c \)

To create a perfect square trinomial from the expression \( x^{2} + 18x + c \), you need to take half of the coefficient of \( x \) (which is 18), square it, and then add that value for \( c \). Half of 18 is 9, and squaring it gives \( 9^2 = 81 \). Therefore, the value of \( c \) that will create a perfect square trinomial is 81. Now, the expression can be rewritten as \( (x + 9)^2 \), which confirms that it is a perfect square trinomial.