Question

Find the number which completes the square.
x^2+24x=c

Answer 1

have the b value then square it (24/2)^2 = 144

since the quadratic is x^2 + 24x - c= 0

to make it a perfect square c = -144 - x - gives a positive

Answer 2

you know, \[(a+b)^2 = a^2 + 2ab + b^2\]


now comparing with above equation,

a=1x
2ab=24x
so, b=12

and ofcourse, b^2 is the"-c" here (minus because you bring it to the LHS later)

so c= -144