50 POINTS PER USER

for fun problem

I already know that the answer is x=2 or 0.346323

but I would like to know HOW to solve it to apply to future problems
 the
question is

\(x^x=2x\)

solve for x

SHOW ALL WORK, answers that I think have insuficient work will be asked for clarification

Verified Answer :

Solve is in the picture

Two lines

Good luck :)

View image Nümerik
View image Nümerik

Hey there, Lets solve this problem step by step. 

First of all, set the given factor '(2 + x)' equal to zero and attempt to solve. 

\(2 + x = 0\)

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the given equation.

\(2 + -2 + x = 0 + -2\) 

Combine like terms:

\(2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2\)

Ask: When will x(x−2) equal zero?

2. Answer: When x=0 or x−2=0

3. Solve each of the 2 equations above: 

\(x=0,2\)