Determine what c-value will create a perfect square trinomial for the following expression: \( x^{2}-15 x+c \)

To create a perfect square trinomial from the expression \( x^{2}-15x+c \), we need to complete the square. The c-value is determined by taking half of the coefficient of the x term, which is -15. Half of -15 is -7.5, and squaring it gives us \( (-7.5)^2 = 56.25 \). Therefore, the c-value that will make this a perfect square trinomial is 56.25. A perfect square trinomial can be factored as \( (x - 7.5)^2 \) when \( c = 56.25 \). This means \( x^{2}-15x+56.25 = (x - 7.5)(x - 7.5) \), demonstrating a beautiful symmetry in the algebra!