Call the number : a
We have : [tex]a^{2} - 15 = 2a[/tex]
[tex]- > a^{2} - 2a = 15 - > a(a-2) = 15[/tex]
Now, we list all the numbers that can be multiplied to get 15 :
1 x 15 (and reverse)
3 x 5 (and reverse)
-1 x (-15) (reverse)
-3 x (-5) (a l s o r e v e r s e)
We substitute in :
If a = 1 -> a(a-2) = 1 x (-1) = -1 (not equal 15)
If a = 3 -> a(a-2) = 3 x 1 = 3 (not equal 15)
If a = -1 -> a(a-2) = -1 x (-3) = -3 (also not equal 15)
And if a = -3 -> a(a-2) = -3 x (-5) = 15 (satisfied)
So, the number is -3
Recheck : -3(squared) - 15 = 9 - 15 = -6
Twice of -3 = -6
[tex]========================================[/tex]
First of all, let the unknown number be z.
Then, "the square of z" means "z squared" which is the same as "z times z" or just z².
Now, "fifteen less than the square of z" means we subtract 15 from z²:
z²-15
Then, this equals twice the number, or 2 times z:
z²-15=2z
[tex]========================================[/tex]
:-)
