I never learned this is Algebra I and Its due by tomorrow, I dont understand Quadratic Equations what-so-ever,help.
Hello Emma! Your equation is quadratic, that is of the form ax^2 + bx + c = 0
where a = 1, b = -14, and c = 24. so we have: x^2 - 14x + 24 = 0
since a = 1 we factor c ( 24) and we add the factors to see if they add up to b (-14).
notice that c is positive =>this means that the two factors were looking for have the same sign.
also since b is negative we know that the larger and hence both of the factors in question are negative.
Now we seek two negative numbers whose product is 24 and whose sum is -14.
fgactoring 24 we get: -1*-24 whose sum is -25 no good. next we try -2*-12 whose sum is -14 <= BINGO!
Now we write: x^2 - 14x + 24 =0
(x - 2) (x - 12) = 0
so set each factor to zero: x-2 = 0 ; x - 12 =0
Finally solve the two resulting linear equations to get: x = 2 ,and x = 12.
I am a math PhD from UW and while both of these earlier answers are good, they show that x^2 - 14x + 24=0 was an unfair question on 8/30, so early in Algebra I!
Maybe it was a pre-test to see how much factoring you got in Pre-algebra.... Not enough, right? :+)
Let's see; we need x^2 - 14x + 24 to factor into (x - d) *(x -e) so that
d*e is 24 and d + e is 14, because x^2 - (d+e)*x + d*e must equal the given left side
and the factors of 24 that work are d=12 and e=2
[we know both linear factors have minus signs because of the -14 and the +24]
so (x - 12)*(x - 2) = 0, which makes both linear factors = zero: x -12 = 0 & x-2=0,
so x = 12 and x = 2 are the quadratic's solutions.
Altho this question is long past, if you have similar ones in future, shoot 'em to me, nearby in Poulsbo, WA.
Quadratic Equestion: ax2 + bx + c = 0
our equestion : x2 - 14x + 24 =0
therefore, a=1, b= -14, c= 24
Factor c to get, product= 24 and sum= -14 (c is +ve: two factors were looking for have the same sign.)
factor: (-2) and (-12) which has sum= -14 and product= 24
x2 - 14x + 24 =0
x(x - 12) - 2(x - 12) = 0
(x- 12)* (x- 2) = 0
x- 12=0 and x-2= 0
solvinf the linear equations we get,
x=12 and x=2