How do you solve 1/2(x-4)^2+3=11?
1 Answer
May 7, 2017
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
