Solving exponential equation y = e^(-x) -x + 1

[cruxxfay]

y = e^(-x) -x + 1

I am told to find the x-intercept so:

0 = e^(-x) - x +1

I have no idea what to do next, I tried to cancel out the denominator by multiplying everything by e^x so it becomes

1 - xe^(x) + e^(x) = 0
1 - e^(x) [x+1] = 0

I am stuck here, can anyone please help me out a bit here

[maggiemagnet]

y = e^(-x) -x + 1

I am told to find the x-intercept so:

0 = e^(-x) - x +1

I have no idea what to do next

Me either! At first I thought "maybe try like this?":

x - 1 = e^-x

But this is "algebraic" on the left side and "transcendental" on the right side, so I don't know how this could be solved with algebra. Are you maybe supposed to do this numerically? The solution (on my calculator) is at about x = 1.2784645 (so y = 0.2784645).

[cruxxfay]

Well this is a calculator paper so I suppose I can use a graph...but the answer says 'Attempt to solve this numerically' so I thought there would be a way to solve this.

[maggiemagnet]

Well this is a calculator paper ... the answer says 'Attempt to solve this numerically' so I thought there would be a way to solve this.

"Numerically" means like they show in the link. They're telling you to do this numerically because you can't do this algebraically (that is, "exactly"). Numerical is the best you can do.

Have they taught you any particular methods to use for doing this numerically? The lesson at the link I gave you shows two ways. Would one of them maybe be okay by your teacher?