Question

solve the equation by making the appropriate substitution: (2x-2)^2-10(2x-2)+21=0

Answer 1

Gee, notice we have a polynomial in \(2x-2\)... I bet we could let \(u=2x-2\) to simplify it.

Answer 2

thats what i was thinking, but not sure exactly how to work it out from there

Answer 3

Well, let's replace all instances of \(2x-2\) with its replacement \(u\):$$u^2-10u+21=0$$Can you factor this now?

Answer 4

yes

Answer 5

Hint: \(-7-3=10,-7\times-3=21\)

Answer 6

Okay, factor and then solve the equation for \(u\) :-)

Answer 7

3=2x-2 which is 5=2x which is 5/2=x or 7=2x-2 which is 9=2x which is 9/2=x: is this right?