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

The answer to x^2+sqrt(2x)= 1/2 is x\approx 0.11812…

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

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

x \approx 0.11812 \dots

Solution steps

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

Multiply both sides by

2

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

Simplify

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

Remove square roots

8 x = 1 - 4 x^{2} + 4 x^{4}

Solve

8 x = 1 - 4 x^{2} + 4 x^{4} : x \approx 0.11812 \dots, x \approx 1.49256 \dots

x \approx 0.11812 \dots, x \approx 1.49256 \dots

Verify Solutions:

x \approx 0.11812 \dots

True

, x \approx 1.49256 \dots

False

The solution is

x \approx 0.11812 \dots

x, x - x + 23 = - 3

\frac{2 - 3 x}{2 1 - x} = 0

5 x + 6 = 1

6 x = 36 x^{2} + 2 x - 10

3 x + 14 = 5 x + 2

What is the answer to x^2+sqrt(2x)= 1/2 ?
The answer to x^2+sqrt(2x)= 1/2 is x\approx 0.11812…
Solve for x: x^2+sqrt(2x)= 1/2
The solution is x\approx 0.11812…