Find the​ number(s).

Question

The square of the difference between a number and 7 is 81 . Find the​ number(s).

Answer 1

(x-7)^2=81

expand the left side

x^2 -14x +49 = 81

x^2 -14x +49-81 = 0

x^2 -14x - 32 = 0

either factor, complete the square or use the quadratic formula

(x-16)(x+2) =0

set each factor equal to zero and solve for x

x-16= 0

x+2 = 0

x= 16 or -2

complete the square

x^2-14x + 49 = 32 + 49

(x-7)^2 = 81

x-7 = + or - 9

x = 7+9 or 7-9

x = 16 or -2

quadratic formula:

x = 14/2 + or - (1/2)sqr(14^2 + 4(32))

x = 7 + or - .5sqr(196 + 128)

x = 7 + or - .5(18)

x = 7 + or - 9

x = 16 or -2