SOLUTION: Please help me! Find all real numbers or imaginary solutions to each equation. x^-2-9x^-1+18=0 I have seen these types of probelms but never with the negative power. I can use a

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Please help me! Find all real numbers or imaginary solutions to each equation. x^-2-9x^-1+18=0 I have seen these types of probelms but never with the negative power. I can use a      Log On


   

Question 81732This question is from textbook
: Please help me!
Find all real numbers or imaginary solutions to each equation.
x^-2-9x^-1+18=0
I have seen these types of probelms but never with the negative power. I can use all the help you have. Thanks in advance. This question is from textbook

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
x^-2-9x^-1+18=0

Change the negative exponents to fractions:
1%2F%28x%5E2%29+-9%281%2Fx%29+%2B18+=+0

Then multiply both sides of the equation by the LCD, which is +x%5E2:
x%5E2%2A%281%2F%28x%5E2%29%29+-x%5E2%2A%289%281%2Fx%29%29++%2Bx%5E2%2A+18+=+x%5E2%2A0
1+-9x+%2B+18x%5E2+=+0
18x%5E2+-9x%2B1=0

This factors into
+%286x-1%29%283x-1%29+=0

First solution:
6x-1=0
6x=1
x= 1/6

Second solution:
3x-1=0
3x=1
x=1/3

R^2 at SCC