What is the answer to x=1+x^{0.5} ?

The answer to x=1+x^{0.5} is x=(3+5^{1/2})/2

Solve for x: x=1+x^{0.5}

The solution is x=(3+5^{1/2})/2

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x = 1 + x^{0.5}

x = \frac{3 + 5 ^{\frac{1}{2}}}{2}

Decimal Notation

x = 2.61803 \dots

Solution steps

x = 1 + x^{0.5}

Remove square roots

x^{2} - 2 x + 1 = x

Solve

x^{2} - 2 x + 1 = x : x = \frac{3 + 5 ^{\frac{1}{2}}}{2}, x = \frac{3 - 5 ^{\frac{1}{2}}}{2}

x = \frac{3 + 5 ^{\frac{1}{2}}}{2}, x = \frac{3 - 5 ^{\frac{1}{2}}}{2}

Verify Solutions:

x = \frac{3 + 5 ^{\frac{1}{2}}}{2}

True

, x = \frac{3 - 5 ^{\frac{1}{2}}}{2}

False

The solution is

x = \frac{3 + 5 ^{\frac{1}{2}}}{2}

x^{2} + 9 = 1 - x

(x^{2} - 15)^{\frac{1}{2}} = 7

x + 1 = - 4

(x - 1)^{\frac{2}{3}} = 0

What is the answer to x=1+x^{0.5} ?
The answer to x=1+x^{0.5} is x=(3+5^{1/2})/2
Solve for x: x=1+x^{0.5}
The solution is x=(3+5^{1/2})/2