## anonymous 5 years ago The given equation involves a power of the variable. Find all real solutions of the equation. 8x^2-64=0

1. slaaibak

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

2. anonymous

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

3. slaaibak

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)

4. anonymous

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

5. anonymous

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...

6. anonymous

and since $8=4\times 2$ $\sqrt{8}=\sqrt{4}\times \sqrt{2}=2\sqrt{2}$

7. anonymous

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

8. anonymous

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