Question

How do you solve `1/2(x-4)^2+3=11`?

Answer 1

`x=0" or " x=8`

Explanation:

`color(blue)"Isolate " (x-4)^2" on the left side"`

`"subtract 3 from both sides"`

`1/2(x-4)^2cancel(+3)cancel(-3)=11-3`

`rArr1/2(x-4)^2=8`

`"multiply both sides by 2"`

`cancel(2)xx1/cancel(2)(x-4)^2=2xx8`

`rArr(x-4)^2=16larr(x-4)^2" isolated on left"`

`color(blue)"take the square root of both sides"`

`sqrt((x-4)^2)=color(red)(+-)sqrt16larr" note plus or minus"`

`rArrx-4=+-4`

`"add 4 to both sides"`

`xcancel(-4)cancel(+4)=+-4+4`

`rArrx=4+-4larrcolor(red)" 2 solutions"`

`rArrx_1=4-4=0" or " x_2=4+4=8`