What is the answer to x= 1/3 x^{1/2}+1 ?

The answer to x= 1/3 x^{1/2}+1 is x=(19+37^{1/2})/(18)

Solve for x: x= 1/3 x^{1/2}+1

The solution is x=(19+37^{1/2})/(18)

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x = \frac{1}{3} x^{\frac{1}{2}} + 1

x = \frac{19 + 3 7 ^{\frac{1}{2}}}{18}

Decimal Notation

x = 1.39348 \dots

Solution steps

x = \frac{1}{3} x^{\frac{1}{2}} + 1

Multiply both sides by

3

x \cdot 3 = \frac{1}{3} x^{\frac{1}{2}} \cdot 3 + 1 \cdot 3

Simplify

x \cdot 3 = x^{\frac{1}{2}} + 3

Remove square roots

9 x^{2} - 18 x + 9 = x

Solve

9 x^{2} - 18 x + 9 = x : x = \frac{19 + 3 7 ^{\frac{1}{2}}}{18}, x = \frac{19 - 3 7 ^{\frac{1}{2}}}{18}

x = \frac{19 + 3 7 ^{\frac{1}{2}}}{18}, x = \frac{19 - 3 7 ^{\frac{1}{2}}}{18}

Verify Solutions:

x = \frac{19 + 3 7 ^{\frac{1}{2}}}{18}

True

, x = \frac{19 - 3 7 ^{\frac{1}{2}}}{18}

False

The solution is

x = \frac{19 + 3 7 ^{\frac{1}{2}}}{18}

2 x - 1 - x = 0

- \frac{- 2 + - 3 x + 3}{0.5} = 4

3 x - 2 + 2 = x

6 - x = \frac{x + 12}{3}

x + 3 - x + 8 = 0

What is the answer to x= 1/3 x^{1/2}+1 ?
The answer to x= 1/3 x^{1/2}+1 is x=(19+37^{1/2})/(18)
Solve for x: x= 1/3 x^{1/2}+1
The solution is x=(19+37^{1/2})/(18)