SOLUTION: If twelve is added to six times a number, the result is twenty-eight less than the square of the number. Find all such numbers.

Question 80619: If twelve is added to six times a number, the result is twenty-eight less than the square of the number. Find all such numbers.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

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

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