SOLUTION: Hi, I'm studying for a test and the problem below seems so simple, but I can't figure this out: {{{4/x - 3/(x+1) = 7}}} I multiplied by the lcd and got: 7x^2 + 6x - 4

Algebra ->  Equations -> SOLUTION: Hi, I'm studying for a test and the problem below seems so simple, but I can't figure this out: {{{4/x - 3/(x+1) = 7}}} I multiplied by the lcd and got: 7x^2 + 6x - 4       Log On


   

Question 360025: Hi, I'm studying for a test and the problem below seems so simple, but I can't figure this out:
4%2Fx++-++3%2F%28x%2B1%29+++=+7
I multiplied by the lcd and got:
7x^2 + 6x - 4 = 0
I tried using the quadratic formula and got:
%28-6+%2B+sqrt%28-76%29%29%2F14
%28-6+-+sqrt%28-76%29%29%2F14
I get confused when I get a negative number in a square root, because we're learning about complex numbers in the same chapter so I don't understand why I can simplify this without using an imaginary number.
The answer on the review sheet is:
x+=+%28-3+-+sqrt%2837%29%29%2F7
x+=+%28-3+%2B+sqrt%2837%29%29%2F7
I honestly don't know how to get there. I simplified the sqrt(-76) and got 2sqrt(38) so how I'm supposed to end up with 37 in the sqrt has me really lost.
Please share your knowledge with me! I'm a little worried after struggling with this for a while now :-/
Thanks for your time.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
it appears that you missed something in the QF

b^2-4ac = 6^2 - (4)(7)(-4) = 36 - (-112) = 148 = 4 * 37