Question

What must be added to 9x2 - 24x + 10 to
make it a whole square?​

Answer 1

suppose we add k in expression to make it whole square

so, 9x2 - 24x + 10 + k = (ax+b)^2

9x2 - 24x + 10 + k = a^2 * x2 + 2*a*b*x + b^2

compare both side of equation

a^2 = 9, so a = 3,-3

2*a*b = - 24

so if a = 3, b = -4, otherwise a=-3, b=4

and 10+k = b^2

10+ k = 16

so k = 6

perfect square is (3x-4)^2