Solve by factoring:?

x2 – 9x = -8

x2 – 9x +8 =0

x2 - 8x - x + 8 =0

x(x-8) -1(x-8)=0

(x-1) (x-8) =0

(x-1)=0 or (x-8)=0

x = 8 or 1

x^2 - 9x = -8
x^2 - 9x + 8 = 0
so (x-8)(x-1) = 0
therefoe x = 8 or x = 1

x2-9x= -8
bring the -8 to the LHS
x2-9x+8=0
x2-8x-x+8=0
x(x-8)-1(x-8)=0
(x-1)(x-8)=0
x=1 or x=8

So, you want to set the whole thing to 0.
x^2-9x+8=0

You kind of just try the different factors for 8:
Either 1 and 8 or 2 and 4.

1 and 8 seem more likely to get 9.
Its -9, though, so it's possible that -1+-8 or -1-8=9
and that (-1)*(-8)=+8 (since the negatives cancel out).

So, now we have (x-1)(x-8)=0
Set each factor to zero, so x-1=0, x=1
and x-8=0, x=8.

x can be 1 or 8.

Note: this problem is easier to understand when you check by foiling (x-1)(x-8) to get x^2-9x+8.

Hope all this helps!

x² − 9x = -8 ⇒ x² − 9x + 8 = 0

x² − 9x + 8 = (x − 1)(x − 8) = 0 ⇒ (x − 1) = 0 or (x − 8) = 0, so x = 1 or 8

x^2 - 9x = -8
x^2 - 9x + 8 = 0
(x - 8)(x - 1) = 0

x - 8 = 0
x = 8

x - 1 = 0
x = 1

∴ x = 8 , 1

(x-8)(x-1)

x² - 9x + 8 = 0
(x - 8)(x - 1) = 0
x = 1, 8