SOLUTION: I need to solve the following quadratic equation using the quadratic formula and I am just not getting it. Please show me the steps. Thank you. 3x^-x-1=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need to solve the following quadratic equation using the quadratic formula and I am just not getting it. Please show me the steps. Thank you. 3x^-x-1=0      Log On


   

Question 107830: I need to solve the following quadratic equation using the quadratic formula and I am just not getting it. Please show me the steps. Thank you.
3x^-x-1=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 3%2Ax%5E2-x-1=0 ( notice a=3, b=-1, and c=-1)





x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A3%2A-1+%29%29%2F%282%2A3%29 Plug in a=3, b=-1, and c=-1




x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A3%2A-1+%29%29%2F%282%2A3%29 Negate -1 to get 1




x+=+%281+%2B-+sqrt%28+1-4%2A3%2A-1+%29%29%2F%282%2A3%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)




x+=+%281+%2B-+sqrt%28+1%2B12+%29%29%2F%282%2A3%29 Multiply -4%2A-1%2A3 to get 12




x+=+%281+%2B-+sqrt%28+13+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




x+=+%281+%2B-+sqrt%2813%29%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%281+%2B-+sqrt%2813%29%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


x+=+%281+%2B+sqrt%2813%29%29%2F6 or x+=+%281+-+sqrt%2813%29%29%2F6



Now break up the fraction



x=%2B1%2F6%2Bsqrt%2813%29%2F6 or x=%2B1%2F6-sqrt%2813%29%2F6



Simplify



x=1%2F6%2Bsqrt%2813%29%2F6 or x=1%2F6-sqrt%2813%29%2F6



So the solutions are:

x=1%2F6%2Bsqrt%2813%29%2F6 or x=1%2F6-sqrt%2813%29%2F6