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=$\frac{-b+/- \sqrt{b^2-4ac} }{2a}$

a=1
b=-11
c=-80
u=$\frac{-(-11)+/- \sqrt{(-11)^2-4(1)(-80)} }{2(1)}$
u=$\frac{11+/- \sqrt{121+320} }{2}$
u=$\frac{11+/- \sqrt{441} }{2}$
u=$\frac{11+/-21 }{2}$
u=$\frac{32}{2}$ or $\frac{-10}{2}$
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