en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

2 x e^{x^{2}} = x^{2} e^{x^{2}}

Solution

x = 0, x = 2

Solution steps

2 x e^{x^{2}} = x^{2} e^{x^{2}}

Subtract

x^{2} e^{x^{2}}

from both sides

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

Simplify

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

Factor

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

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

Using the Zero Factor Principle:

If

ab = 0

then

a = 0

or

b = 0

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

Solve

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

No Solution for

x \in R

Solve

2 - x = 0 : x = 2

x = 0, x = 2

Popular Examples

216 = 6^{2 x - 15}

2^{x^2-5x}= 1/64

2^{x^{2} - 5 x} = \frac{1}{64}

4^{x} - 1 0^{x} = 2 5^{x}

x^{log_{10}(x)}=10^4

x^{l o g_{10} (x)} = 1 0^{4}

(sqrt(6))^{8x}=216^{x-3}

(6)^{8 x} = 21 6^{x - 3}

Frequently Asked Questions (FAQ)

What is the answer to 2xe^{x^2}=x^2e^{x^2} ?
The answer to 2xe^{x^2}=x^2e^{x^2} is x=0,x=2