How do you solve the equation #2/3(x+8)^2-66=0#?

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Answer 1 · 2017-07-18T13:21:15

#x=-8+-3sqrt11#

#2/3(x+8)^2-66=0#

#2/3(x+8)^2=66# #->#add #66# to both sides

#color(blue)(3/2)*2/3(x+8)^2=66*color(blue)(3/2)# #->#multiply both sides by #3/2#

#(x+8)^2=99#

#x+8=+-sqrt99# #->#take the square root of both sides

#x+8=+-3sqrt11# #->#simplify the radical

#x=-8+-3sqrt11# #->#subtract #8# from both sides

Answer 2 · 2017-07-18T15:41:45

#color(magenta)(x=-8+3sqrt11 or x=-8-3sqrt11#

#2/3(x+8)^2-66=0#

#:.2/3(x^2+16x+64)-66=0#

#:.2/3x^2+32/3x+128/3-66=0#

#:.2/3x^2+32/3x+128/3-198/3=0#

#:.2/3x^2+32/3x-70/3=0#

multiply both sides by 3

#:.2x^2+32x-70=0#

#:.2(x^2+16x-35)=0#

#:.x^2+16x-35=0#

#:.x=(-b+-sqrt(b^2-4ac))/(2a)#

#a=1,b=16,c=-35#

#:.x=(-16+-sqrt(16^2-4(1)(-35)))/((2)(1))#

#:.x=(-16+-sqrt(256+140))/2#

#:.x=(-16+-sqrt(396))/2#

#x=(-16+-sqrt(11*3*3*2*2))/2#

#:.x=(-16+-6sqrt(11))/2#

#:.cancel(-16)^color(magenta)(-8)/cancel2^color(magenta)(1)+-(cancel(-6)^color(magenta)(-3)sqrt(11))/cancel2^color(magenta)(1)#

#:.-8+-3sqrt11#

#:.color(magenta)(x=-8+3sqrt11,x=-8-3sqrt11#