Question

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

Answer 1

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`

Answer 2

Solve is in the picture

Two lines

Good luck :)