SOLUTION: find all real solutions of the equation: 1 over x cubed plus 4 over x squared plus 4 over x equals zero I didn't understand what all of the signs meant so i wrote out all of

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: find all real solutions of the equation: 1 over x cubed plus 4 over x squared plus 4 over x equals zero I didn't understand what all of the signs meant so i wrote out all of       Log On


   

Question 102468This question is from textbook algebra and Trigonmetry
: find all real solutions of the equation:
1 over x cubed plus 4 over x squared plus 4 over x equals zero
I didn't understand what all of the signs meant so i wrote out all of the words This question is from textbook algebra and Trigonmetry

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I think this is what you mean.
1%2Fx%5E3%2B4%2Fx%5E2%2B4%2Fx=0
First step, get rid of any x expressions in the denominators by multiplying both sides by x^3.
x%5E3%2A%281%2Fx%5E3%2B4%2Fx%5E2%2B4%2Fx%29=x%5E3%2A%280%29
x%5E3%2A%281%2Fx%5E3%29%2B%284%2Ax%5E3%2Fx%5E2%29%2B%284%2Ax%5E3%2Fx%29=0Distributive property
1%2Ax%5E%283-3%29%2B4%2Ax%5E%283-2%29%2B4%2Ax%5E%283-1%29=0Dividing same base, subtract exponents
1%2B4x%2B4x%5E2=0 Simplify.
4x%5E2%2B4x%2B1=0 A quadratic equation.
x%5E2%2Bx%2B1%2F4=0 Divide both sides by 4.
%28x%2B1%2F2%29%5E2=0 Factor the quadratic equation.
sqrt%28%28x%2B1%2F2%29%5E2%29=0 Take the square root of both sides.
x%2B1%2F2=0
x=-1%2F2
Check your answer using the value for x and your original equation.
1%2Fx%5E3%2B4%2Fx%5E2%2B4%2Fx=0
x%5E3=-1%2F8
highlight%281%2Fx%5E3=-8%29
x%5E2=1%2F4
1%2Fx%5E2=4
highlight%284%2Fx%5E2=16%29
x=-1%2F2
1%2Fx=-2
highlight%284%2Fx=-8%29
Now plug those values into your original equation.
highlight%281%2Fx%5E3%29%2Bhighlight%284%2Fx%5E2%29%2Bhighlight%284%2Fx%29=0
-8%2B16-8=0
0=0
Good answer.