Answer:
[tex]u^2-u-6=0[/tex]
where
[tex]u=(x-4)[/tex]
Step-by-step explanation:
we have
[tex](x-4)^2-(x-4)-6=0[/tex]
Let
[tex]u=(x-4)[/tex]
substitute in the expression above
[tex](u)^2-(u)-6=0[/tex]
Solve for u
Complete the square
[tex](u^2-u+0.25)=6+0.25[/tex]
[tex](u^2-u+0.25)=6.25[/tex]
Rewrite as perfect squares
[tex](u-0.5)^2=6.25[/tex]
square root booth sides
[tex]u-0.5=\pm2.5[/tex]
[tex]u=0.5\pm2.5[/tex]
[tex]u_1=0.5+2.5=3[/tex]
[tex]u_2=0.5-2.5=-2[/tex]
Solve for x
Remember that
[tex]u=(x-4)[/tex]
For u=3
[tex]3=(x-4)[/tex] ----> [tex]x=7[/tex]
For u=-2
[tex]-2=(x-4)[/tex] ----> [tex]x=2[/tex]
