solve using any method. x^2-7x+6

Question

solve using any method.   x^2-7x+6

anonymous · Answer

you can factor this 

multiply the first and second number then find all factors of that number

1*6=6


1*6
2*3
3*2
6*1
-1*-6
-2*-3
-3*-2
-6*-1

one of thee factors can add up to -7

anonymous · Answer

let me rephrase the first part 

multiply the first coefficient (the numbernext to x^2) with the 3rd coefficient (6 in this case)*

anonymous · Answer

-6+-1=-7

anonymous · Answer

so now split the middle term into -6 and -1

anonymous · Answer

$$x^2-6x-x+6$$ correct?

now you can group the first two and second two terms
$$(x^2-6x)+(-x+6)$$

if you pull an x out of the first group and a -1 out of the second group you get this

$$x(x-6)+-1(x-6)$$

one factor is what is in both parenthesis (x-6). the other is the outside (x-1)

$$(x-1)(x-6)$$

anonymous · Answer

now in order for these to = 0

$$(x-1)(x-6)=0$$

x-1=0 and or x-6=0

if you solve these you get

x=6 and x=1. these are your roots

rayford · Answer

dear lord thank you!!!

anonymous · Answer

yes the more you do these rayford, the less you have to do it this way. You'll start to see it right away without having to do this systematic method

rayford · Answer

i will! i have the drive for this!!