en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

e^{-x}-2xe^x=0

Solution

e^{- x} - 2 x e^{x} = 0

Solution

x = \frac{W _{0} ( 1 )}{2}

+1

Decimal Notation

x = 0.28357 \dots

Solution steps

e^{- x} - 2 x e^{x} = 0

Factor

e^{- x} - 2 x e^{x} : e^{- x} (1 - 2 e^{2 x} x)

e^{- x} (1 - 2 e^{2 x} x) = 0

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

e^{- x} = 0 or 1 - 2 e^{2 x} x = 0

Solve

e^{- x} = 0 :

No Solution for

x \in R

Solve

1 - 2 e^{2 x} x = 0 : x = \frac{W _{0} ( 1 )}{2}

x = \frac{W _{0} ( 1 )}{2}

Popular Examples

5^x+5^{x+1}=750

5^{x} + 5^{x + 1} = 750

(1/8)^x=16^{x-3}

(\frac{1}{8})^{x} = 1 6^{x - 3}

(0.5)^{x} = 2

e^{t} = 1

e^{x} = e^{3 x + 8}

Frequently Asked Questions (FAQ)

What is the answer to e^{-x}-2xe^x=0 ?
The answer to e^{-x}-2xe^x=0 is x=(\W_{0}(1))/2