SOLUTION: Okay, I need to solve for this using quadratic equations, I have the problem and the answer, can't make the two connect. f(x)=7/x + 7/x+4, f(x) = 1 Result should be 5(+-)(sq.r

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Okay, I need to solve for this using quadratic equations, I have the problem and the answer, can't make the two connect. f(x)=7/x + 7/x+4, f(x) = 1 Result should be 5(+-)(sq.r      Log On


   

Question 1766: Okay, I need to solve for this using quadratic equations, I have the problem and the answer, can't make the two connect.
f(x)=7/x + 7/x+4, f(x) = 1 Result should be 5(+-)(sq.rt of) 53
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
assuming your equations are f%28x%29+=+%287%2Fx%29+%2B+%287%2F%28x%2B4%29%29 and f%28x%29+=+1, then ignore the f(x) bit and just put y instead...so y equals the first one and also the second one, so the two equations are equal to each other, ie...
%287%2Fx%29+%2B+%287%2F%28x%2B4%29%29+=+1
do fractions on this, to give...
7%28x%2B4%29+%2B+7%28x%29+=+x%28x%2B4%29
then simplify out and collect terms (being careful with negative signs) to give...
x%5E2+-+10x+-+28+=+0
Solve this with the Quadratic formula to give
x+=+%2810+%2B-+%28sqrt%28212%29%29%29%2F%282%29
sqrt%28212%29 is also %28sqrt%284%2A53%29%29. then take the 4 out, becoming 2 and then cancel the fraction, which gives
x+=+5+%2B-+%28sqrt%2853%29%29
cheers
Jon.