SOLUTION: Hi, I am studying for a test and could really use some help with this problem. I know that I can use either the quadratic equation, completing the square, or factoring. {{{x^2+m^2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Hi, I am studying for a test and could really use some help with this problem. I know that I can use either the quadratic equation, completing the square, or factoring. {{{x^2+m^2      Log On


   

Question 70858This question is from textbook College Algebra Essential
: Hi, I am studying for a test and could really use some help with this problem. I know that I can use either the quadratic equation, completing the square, or factoring.
x%5E2%2Bm%5E2=2mx%2B%28nx%29%5E2
Thank you so much for your help! This question is from textbook College Algebra Essential

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're on the right track, we're going to complete the square
x%5E2%2Bm%5E2-2mx=cross%282mx-2mx%29%2B%28nx%29%5E2subtract 2mx from both sides (edit: sorry you're not supposed to subtract m^2 on the left hand side)
Now we need to find 2 terms which add to -2mx and multiply to m^2, these two are -m and -m, so the factors are
%28x-m%29%28x-m%29=n%5E2%2Ax%5E2
%28x-m%29%5E2=n%5E2%2Ax%5E2Which can be also written as this
sqrt%28%28x-m%29%5E2%29=sqrt%28n%5E2%2Ax%5E2%29Take square root of both sides
x-m=nxSubtract nx and add m to both sides
x%281-n%29=mFactor out an x
%28x%2Across%281-n%29%29%2Fcross%281-n%29=m%2F%281-n%29Divide both sides by (1-n)
x=m%2F%281-n%29
To verify this let m and n be any numbers (preferably small numbers to make it easy) and this should be equivalent to the given problem.
Check let m=1, n=2, and plug in x=1
x=1%2F%281-2%29=-1
%28-1%29%5E2%2B1%5E2=2%2A1%2A%28-1%29%2B%282%2A1%29%5E2
2=2 So the answer checks out