quadratic equations..

[shefflebat]

yeah..i don't exactly get the factor zero product rule. it is confusing. and i have to solve a lot of equations using it, so it would be nice to have a grasp on it..how would i solve something like 3x^2 + 5x = 22 using the factor zero product rule?

completing the square is slightly easier for me to understand, but i still am having trouble solving a lot of equations using it. can someone show me how to solve something like x^2 + 5x = 84 by completing the square?

we aren't supposed to use the quadratic formula, which seems like the easiest way to me..so..yes. some help would definitely be appreciated.

 

[Guest]

The zero product rule just means solving by factoring, ie needs to be placed in the form of (x -4)(x+3)

the solutions rely on each of these being equal to zero (x-4) =0 or (x+3)=0

3x^2 + 5x = 22

3x^2 + 5x - 22 =0

(x......) (x......) = the above

need to have a 3x to make the 3x^2, and look at the factors of 22 = 2 .11

(3x-2)(x+11) ... or ... (3x +11) (x-2)

and you cans see the correct solution is
(3x + 11) (x-2)

then
x^2 + 5x = 84

look at the value in front of the "x" term ie the 5, take 1/2 of this = 2.5

then square the 2.5 value = 2.5 x 2.5 = 6.25

x^2 +5x +6.25 = 84 + 6.25 ie we have added the square to both sides

(x +2.5)^2 = 84 + 6.25

(x +2.5)^2 = 90.25

(x +2.5) = sqrt 90.25

x + 2.5 = + - 9.5

back to you

 

[Denis]

If you're not too tired, you could do a http://www.google.com search
on "factor zero product rule" and on "completing the square".