I need help on my Algebra homework!?

Question

I need to factor out this equation completely.

x squared-21x+84=0

I know how to do it, I just can't find the factors of 84 that will add to -21. Help, please!

Answer 1

-b +or- square root of (b squared - 4ac) all divided by 2a

21 + or - square root of (441 - 4(1)(84) all divided by 2(1)

21 + or minus square root of (441-336) all divided by 2

21 + or minus square root of 105 all divided by 2

(21 + 10.25)/2 = 31.25 / 2 = 15.75

(21- 10.25 ) /2 = 10.75 /2 = 5.375

Of course these are just approximates - you will need to use square root of 105 instead of decimal approximates

Answer 2

This one doesn't have integer roots, so factor using "completing the square":
x^2 - 21x + 84 = 0
x^2 - 21x + (21/2)^2 - (21/2)^2 + 84 = 0
(x - 21/2)^2 + (336 - 441)/4 = 0
(x - 21/2)^2 -105/4 = 0
(x - (1/2)(21 - √105))(x - (1/2)(21 + √105))

Answer 3

14 and 16

Answer 4

x(x-21)+84 = 0

I'm not sure if this is right but it's the best I got?

Answer 5

you can say its not possible or theres this formula i think just google: coordinate geometry

Answer 6

im pretty sure x = 4!