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

The answer to 1/2 x^2=sqrt(2x)+1 is x\approx 2.55335…

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

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

x \approx 2.55335 \dots

Solution steps

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

Multiply both sides by

2

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

Simplify

x^{2} = 2 2 x + 2

Remove square roots

x^{4} - 4 x^{2} + 4 = 8 x

Solve

x^{4} - 4 x^{2} + 4 = 8 x : x \approx 0.41688 \dots, x \approx 2.55335 \dots

x \approx 0.41688 \dots, x \approx 2.55335 \dots

Verify Solutions:

x \approx 0.41688 \dots

False

, x \approx 2.55335 \dots

True

The solution is

x \approx 2.55335 \dots

\frac{- 2 x ^{2} + 100}{100 - x ^{2}} = 0

2 x^{\frac{1}{2}} - 5 x^{\frac{1}{4}} = 3

x + 3 = 2 x - 1

8 x - 13 = 1

x + 18 = x - 2

What is the answer to 1/2 x^2=sqrt(2x)+1 ?
The answer to 1/2 x^2=sqrt(2x)+1 is x\approx 2.55335…
Solve for x: 1/2 x^2=sqrt(2x)+1
The solution is x\approx 2.55335…