we have that
x² + 7x + c
Group terms that contain the same variable
(x² + 7x )+ c
Complete the square. Remember to balance the equation
(x² + 7x+3.5² )+ c-3.5²
Rewrite as perfect squares(x+3.5)²+ c-3.5²
so
c-3.5² must be zero
c-3.5²=0------- c=3.5²------> c=12.25
the answer is
the value of c must be 12.25