Question

xe^-x + e^-x = 0

Answer 1

Solve for x?

Answer 2

yes

Answer 3

\[\Large\bf\sf x\color{#DD4747 }{e^{-x}}+\color{#DD4747 }{e^{-x}}\quad=\quad 0\]
Factor an e^-x out of each term:
\[\Large\bf\sf \color{#DD4747 }{e^{-x}}(x+1)\quad=\quad 0\]

Answer 4

Does that first step make sense?
Understand why there is a +1?

Answer 5

yes

Answer 6

Then to solve for x, we'll use the Zero Factor Property.
We'll set each factor equal to zero and solve for x separately in each case.\[\Large\bf\sf e^{-x}=0,\qquad\qquad\qquad (x+1)=0\]

Answer 7

In the first case, we have an exponential function.
Exponential function never touches the x-axis.
We have no solution for x there.

How bout the other one?
Subtract 1 from each side, yes? :O

Answer 8

x=-1

Answer 9

thank you!

Answer 10

Yesssss, good job \c:/