Question 80619

Let x=the number
x^2= the square of the number; 28 less is x^2-28
Six times the number is 6x and when we add 12 we get 6x+12

We are told that:

6x+12=x^2-28  subtract 6x and also 12 from both sides

6x-6x+12-12=x^2-6x-12-28  collect like terms

0=x^2-6x-40 or x^2-6x-40=0   quadratic in standard form and it can be factored:

(Note: When the A coefficient of a quadratic is 1, then the B coefficient will be the sum of the factors of the C coefficient, if it is factorable.  In this case the factors of -40 that add up to -6 are -10 and +4)

(x-10)(x+4)=0

x=10
and
x=-4

CK
for x=10
6(10)+12=10^2-28
72=72
for x=-4
6(-4)+12=(-4)^2-28
-24+12=16-28
-12=-12


Hope this helps----ptaylor