SOLUTION: hello there, can I get help with this? i need to solve for x! 8x^3/x^5 = 512 and then i need to enter the exact answers in increasing order. x = ? x = ? bye now.

Question 1168255: hello there, can I get help with this?
i need to solve for x!
8x^3/x^5 = 512
and then i need to enter the exact answers in increasing order.
x = ?
x = ?
bye now.

Found 3 solutions by Alan3354, josgarithmetic, Theo:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
8x^3/x^5 = 512
8/x^2 = 512
1/x^2 = 64
x^2 = 1/64
x = 1/8
x = -1/8
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
your equation is 8x^3/x^5 = 512

since x^3 / x^5 is equal to 1/x^2, the equation becomes:

8/x^2 = 512

multiply both sides of the equation by x^2 and divide both sides of the equation by 512 to get:

8/512 = x^2

simplify to get:

1/64 = x^2

solve for x to get:

x = plus or minus (1/8)

those are your solutions.

x = 1/8 or x = -1/8 (correction to previous answer was made here.

if you graphed the equation of y = 8x^3/x^5 and graphed the equation of x = -1/8 and x = 1/8, and then took the intersection of the first equation with the last two, it would look like this.

you can see that the intersection points of the first equation with the second and third equation is at y = 512.

the graph shows the x values of the coordinate points as plus or minus .0125

plus or minus .0125 is equal to plus or minus 1/8.

you can also see from the graph, that the equation of y = 8x^3/x^5 has a vertical asymptote at x = 0.

that's because the equation is undefined at x = 0 because it becomes 0/0.

as the value of x approaches 0 from either to the left of it or to the right of it, the value of y becomes greater and greater as x gets closer and closer to 0.

as 2 examples, consider x = plus or minus .02 and x = plus or minus .01.

when x = plus or minus .02, the value of y = 20,000.

when x = plus or minus .01, the value of y = 80,000.

one more value of x at .005 should cement the progression.

when x = plus or minus .005, the value of y = 320,000

y will get larger and larger when x approaches 0 from either end.

x can never be 0, hence the vertical asymptote at x = 0

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