Question

The given equation involves a power of the variable. Find all real solutions of the equation.
8x^2-64=0

Answer 1

8(x^2 - 8)=0
x=2sqrt(2) or x = -2sqrt(2)

Answer 2

okay. can you show me what you did there? i'm having real trouble understanding this

Answer 3

you first take out the common factor, which is 8:

8(x^2 - 8) = 0

then you use the difference of squares principle:

8(x-sqrt(8))(x+sqrt(8))=0

then x = sqrt(8) or x= -sqrt(8)

simplified it's
x=2sqrt(2) or x = -2sqrt(2)

Answer 4

\[8x^2-64=0\] add 64 to both sides
\[8x^2=64\]
divide both sides by 8
\[x^2=8\]
take the square root
\[x=\pm\sqrt{8}=\pm2\sqrt{2}\]

Answer 5

i think it's coming to me... i get where you get the common factor, then the difference of squares is giving me trouble... but i see what you are doing...

Answer 6

and since \[8=4\times 2\]
\[\sqrt{8}=\sqrt{4}\times \sqrt{2}=2\sqrt{2}\]

Answer 7

how do you know the 2(sqrt)2?? that is really throwing me for a loop.

Answer 8

why isn't the square root of 8 just 2?