SOLUTION: I need to see the steps to solve 1-x^-1-20x^-2=0

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Question 913834: I need to see the steps to solve 1-x^-1-20x^-2=0
Found 3 solutions by josgarithmetic, MathLover1, lwsshak3:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
lowest common denominator is x%5E2, so best suggestion is multiply the left and right members by x%5E2. You will then solve a quadratic equation. Do the first two steps, simplify, and you should understand a fairly predictable solution path. The only reason you might not know how to start is forgotten what negative exponent means.

You are starting with 1-1%2Fx-20%2Fx%5E2=0.
Multiply left and right by x%5E2.........
......in fact when you do this you should find that the quadratic is factorable.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
+1-x%5E-1-20x%5E-2=0
+1-1%2Fx-20%281%2Fx%5E2%29=0
+1x%5E2%2Fx%5E2-1x%2Fx%5E2-20%2Fx%5E2=0
+%28x%5E2-x-20%29%2Fx%5E2=0
+%28x%5E2-x-20%29=0%2Ax%5E2
+x%5E2-x-20=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-20%29%29+%29%2F%282%2A1%29+

x+=+%281+%2B-+sqrt%28+1%2B80%29+%29%29%2F2+

x+=+%281+%2B-+sqrt%28+81%29+%29%29%2F2+

x+=+%281+%2B-+9+%29%2F2+
solutions:

x+=+%281+%2B+9+%29%2F2+
x+=+%281+%2B+9+%29%2F2+
x+=+10%2F2+
x+=+5+
or
x+=+%281+-+9+%29%2F2+
x+=+%281-+9+%29%2F2+
x+=+-8%2F2+
x+=+-4+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+1-x%5E-1-20x%5E-2%29+

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
solve 1-x%5E-1-20x%5E-2=0
let u=x^-1
u^2=x^-2
1-u-20u^2=0
20u^2+u-1=0
(4u+1)(5u-1)=0
u=-1/4=x^-1
-1/4=(1/x)
x=-4
or
u=1/5=x^-1
1/5=1/x
x=5
Check:
f(-4)=1-x^-1-20x^-2
f(-4)=1-1/x-20/x^2
f(-4)=1+1/4-20/16=5/4-5/4=0
f(5)=1-1/5-20/25=4/5-4/5=0
Both zeros check ok