SOLUTION: Directions only said SOlve: (x^2 -2x)^2 -11(x^2 -2x) +24=0

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Question 343922: Directions only said SOlve:
(x^2 -2x)^2 -11(x^2 -2x) +24=0
Found 2 solutions by Jk22, Fombitz:
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
let z=x^2-2x, then z^2-11z+24=0, by Viete (z-3)(z-8)=0
z=3 implies x^2-2x-3=0 => (x-3)(x+1)=0, x=3 or x=-1
z=8 implies x^2-2x-8=0 => (x-4)(x+2)=0, x=4 or x=-2
verif : 3 : (9-6)^2-11*3+24=9-33+24=33-33=0
-1 : (1+2)^2-11*3+24=9-33+24=33-33=0
4 : (16-8)^2-11*8+24=64-88+24=88-88=0
-2 : (4+4)^2-11*8+24=64-88+24=88-88=0
ok.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a substitution, u=x%5E2-2x
%28x%5E2+-2x%29%5E2+-11%28x%5E2+-2x%29+%2B24=0
u%5E2+-11u%2B24=0
%28u-8%29%28u-3%29=0
Two solutions in u:
u-8=0
u=8
x%5E2-2x=8
x%5E2-2x-8=0
%28x-4%29%28x%2B2%29=0
Two solutions in x:
x-4=0
highlight%28x=4%29
.
.
x%2B2=0
highlight%28x=-2%29
.
.
.
u-3=0
u=3
x%5E2-2x=3
x%5E2-2x-3=0
%28x-3%29%28x%2B1%29=0
Two solutions in x:
x-3=0
highlight_green%28x=3%29
.
.
.
x%2B1=0
highlight_green%28x=-1%29
.
.
.
Four solutions: (-2,-1,3,4)