What is the answer to 2/((sqrt(2x+1))+1)=x ?

The answer to 2/((sqrt(2x+1))+1)=x is x\approx 0.77091…

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2/((sqrt(2x+1))+1)=x

\frac{2}{( 2 x + 1 ) + 1} = x

x \approx 0.77091 \dots

Solution steps

\frac{2}{( 2 x + 1 ) + 1} = x

Multiply both sides by

2 x + 1 + 1

\frac{2}{2 x + 1 + 1} (2 x + 1 + 1) = x (2 x + 1 + 1)

Simplify

2 = x (2 x + 1 + 1)

Expand

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

2 = 2 x + 1 x + x

Remove square roots

4 - 4 x + x^{2} = 2 x^{3} + x^{2}

Solve

4 - 4 x + x^{2} = 2 x^{3} + x^{2} : x \approx 0.77091 \dots

x \approx 0.77091 \dots

Verify Solutions:

x \approx 0.77091 \dots

True

The solution is

x \approx 0.77091 \dots

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

d, b = r - r^{2} - d^{2}

[1.38 (64 + x^{2})^{\frac{1}{2}}] - 1 = 0

4 + 2 x - 4 = x

x + 7 x + 52 = 0

What is the answer to 2/((sqrt(2x+1))+1)=x ?
The answer to 2/((sqrt(2x+1))+1)=x is x\approx 0.77091…
Solve for x: 2/((sqrt(2x+1))+1)=x
The solution is x\approx 0.77091…