Question

(x^2-6x)^2-11(x^2-6x)-80=0

Answer 1

ok so

we treat the group (x^2-6x) as u
quadratic formula

for au^2+bu+c=0
u=
`(-b+/- √(b^2-4ac) )/(2a)`

a=1
b=-11
c=-80
u=
`(-(-11)+/- √((-11)^2-4(1)(-80)) )/(2(1))`
u=
`(11+/- √(121+320) )/(2)`
u=
`(11+/- √(441) )/(2)`
u=
`(11+/-21 )/(2)`
u=
`(32)/(2)` or
`(-10)/(2)`
u=16 or -5


x^2-6x=16 or -5
solve each

x^2-6x=16
x^2-6x-16=0
(x-8)(x+2)=0
x=8 or -2

x^2-6x=-5
x^2-6x+5=0
(x-1)(x-5)=0
x=1 or 5

x=-2,1,5, or 8