What is the answer to solvefor x,2xln(x)+x=0 ?

The answer to solvefor x,2xln(x)+x=0 is x= 1/(sqrt(e))

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solvefor x,2xln(x)+x=0

solve for

x, 2 x ln (x) + x = 0

x = \frac{1}{e}

Decimal

x = 0.60653 \dots

Solution steps

2 x ln (x) + x = 0

Move

x

to the right side

2 x ln (x) = - x

Move

x

to the left side

2 x ln (x) + x = 0

Factor

2 x ln (x) + x : x (2 ln (x) + 1)

x (2 ln (x) + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 ln (x) + 1 = 0

Solve

2 ln (x) + 1 = 0 : x = \frac{1}{e}

Verify Solutions:

x = 0

False

, x = \frac{1}{e}

True

The solution is

x = \frac{1}{e}

lo g_{216} (x) = - \frac{1}{3}

lo g_{10} (3 x + 7) = 2

0 = x ln (3 x - 5)

ln (3 x - 5) = 6

lo g_{10} (x) = 0

What is the answer to solvefor x,2xln(x)+x=0 ?
The answer to solvefor x,2xln(x)+x=0 is x= 1/(sqrt(e))