Completing the square and Quadratic formula

Question

Find the values of c and d if the trinomial

x²+18x+c

can be factored as

(x+d)²

Answer 1

(x+d)² = (x+d)(x+d)

Foil

x²+2dx+d² = x² +18x + c

Cross out the x² to simplify then compare the values with x

2dx = 18x; cross out x: 2d = 18 therefore d=9

Plug 9 into the equation above to get c= 81