Could someone explain how to properly (and in the easiest way), simplify:

d = √(x² + (5 - 2x)²/16 )

Thank you! :)

Question

Could someone explain how to properly (and in the easiest way), simplify:

d = √(x² + (5 - 2x)²/16 )

Thank you! :)

anonymous · Answer

So the problem looks like $$d=\sqrt{x^2+(5-2x)^2}/16$$ with the square root being all over 16?

anonymous · Answer

Well, it was $$y ^{2}=(5-2x)^{2}/16  $$

and it got plugged into:

distance equation: 

$$d=\sqrt{x ^{2}+y ^{2}}$$

anonymous · Answer

What I did was expand the (5-2x)^2 and then multiplied the x^2 by 16/16 so I could add the numerators and have all term over 16. From there you can factor and get rid of the 1/16 which becomes 1/4 after you pull it out of the square root. From there, you have a function that really can't be simplified any further.

anonymous · Answer

What was the original problem?  It looks like you have the equation for an ellipse.  I don't see how the distance formula would apply in they way that you used it.

anonymous · Answer

Consider the point (x,y) lying on the graph of the line 2x+4y=5. Let L be the distance from the point (x,y) to the origin (0,0). Write L as a function of x.

anonymous · Answer

I see.  That makes more sense.  And your answer is right.  And, as pjschlotter said, it doesn't really simplify any further.  It's already a function of x, so it doesn't NEED to be simplified any more to be an answer to the question.