SOLUTION: Suppose a and x satisfy x^2 + (1-1/a)x - 1 = 0. Solve for x in terms of a. *That's a quadratic in x

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Suppose a and x satisfy x^2 + (1-1/a)x - 1 = 0. Solve for x in terms of a. *That's a quadratic in x      Log On


   

Question 1086029: Suppose a and x satisfy x^2 + (1-1/a)x - 1 = 0. Solve for x in terms of a.
*That's a quadratic in x
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+%281-1%2Fa%29x++-+1+=+0
use quadratic formula:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ .....you have: a=1, b=%281-1%2Fa%29, and c=-1

x+=+%28-%281-1%2Fa%29+%2B-+sqrt%28+%281-1%2Fa%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+

x+=+%28%281-a%29%2Fa+%2B-+sqrt%28+%28%28a-1%29%2Fa%29%5E2%2B4+%29%29%2F2+

x+=+%28%281-a%29%2Fa+%2B-+sqrt%28+%28%28a-1%29%5E2%2Fa%5E2%29%2B4+%29%29%2F2+

x+=+%28%281-a%29%2Fa+%2B-+sqrt%28+%28%28a-1%29%5E2%2Fa%5E2%29%2B4a%5E2%2Fa%5E2+%29%29%2F2+

x+=+%28%281-a%29%2Fa+%2B-+sqrt%28+%28%28a-1%29%5E2%2B4a%5E2%29%29%2Fsqrt%28a%5E2%29+%29%2F2+

x+=+%28%281-a%29%2Fa+%2B-+sqrt%28a%5E2-2a%2B1%2B4a%5E2%29%2Fa+%29%2F2+

x+=+%28%281-a+%2B-+sqrt%285a%5E2-2a%2B1%29%29%2Fa+%29%2F2+

x+=+%281-a+%2B-+sqrt%285a%5E2-2a%2B1%29%29%2F2a+ for a%3C%3E0