How do you solve the equation #1/3(x+4)^2-1=5#?

1 Answer
Mar 12, 2017

Answer:

#3\sqrt{2}-4#

Explanation:

new/changed values are in #\color(indianred)(\text{this }color)#


#1/3(x+4)^2-1=5#
add 1 to both sides (cancels out the #-1#)...
#1/3(x+4)^2=\color(indianred)(6)#
multiply both sides by 3 (cancels out the #1/3#)...
#(x+4)^2=\color(indianred)(18)#
square root both sides (cancels out square on left)...
#x+4=\color(indianred)(\sqrt{18})#
subtract 4 from both sides (cancels out the #-4#)...
#x=\sqrt{18}\color(indianred)(-4)#


now we have the base result, #x=\sqrt{18}-4#
but this can be simplified...
#\sqrt{18}=\sqrt{\cancel{3}\cdot\cancel{3}\cdot2}=3\sqrt{2}#
therefore, your result is...

#3\sqrt{2}-4#