SOLUTION: I need to solve the equation {{{x^4+4x^3+2x^2=0}}} for all real numbers. This is what i have so far. {{{x^2(x^2+4x+2)=0}}} Then I can set x^2=0 and get x=0 after taking the

Algebra ->  Equations -> SOLUTION: I need to solve the equation {{{x^4+4x^3+2x^2=0}}} for all real numbers. This is what i have so far. {{{x^2(x^2+4x+2)=0}}} Then I can set x^2=0 and get x=0 after taking the       Log On


   

Question 553819: I need to solve the equation x%5E4%2B4x%5E3%2B2x%5E2=0 for all real numbers.
This is what i have so far.
x%5E2%28x%5E2%2B4x%2B2%29=0
Then I can set x^2=0 and get x=0 after taking the square root of both sides.
then the problem that is left is a quadratic so i can use the quadratic formula and get
x=%28-4%2B+or+-sqrt%284%5E2-4%2A1%2A2%29%29%2F%282%2A1%29
after i combine every thing i get x=%28-4%2B+or+-+sqrt%288%29%29%2F2
the answer in the back of the book is -2%2Bor+-+sqrt%282%29
i see how -4 is smiplified down to -2 what i don't understand is how you get the sqrt2 out of sqrt%288%29%2F2. Am i completly off track or did i miss something. please help if you can
thanks Kathleen Nolan
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
You are close!!

%28-4%2B-sqrt%288%29%29%2F2
%28-4%2B-sqrt%284%29%2Asqrt%282%29%29%2F2
%28-4%2B-2%2Asqrt%282%29%29%2F2

Factor the 2 in the numerator:
+%282%28-2%2B-sqrt%282%29%29%29%2F2

Divide out the 2, and you will have the correct answer!!
-2%2B-sqrt%282%29+

You may want to see my FREE website for additional explanation on this topic. The easiest way to find the website is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. Near the bottom of this page is a link that takes you to my Homepage. On my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra" and look in Chapter 5 for the section on Reducing Fractions with Radicals. There is also an explanation in "Intermediate Algebra", "Chapter 3." I think you will really like the "Math in Living Color" pages that go with these sections.

If you need to contact me, send me an Email at rapaljer@seminolestate.edu.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus