What is the answer to 3x+sqrt(3x+1)=x ?

The answer to 3x+sqrt(3x+1)=x is x=-1/4

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3x+sqrt(3x+1)=x

3 x + 3 x + 1 = x

x = - \frac{1}{4}

Decimal

x = - 0.25

Solution steps

3 x + 3 x + 1 = x

Remove square roots

3 x + 1 = 4 x^{2}

Solve

3 x + 1 = 4 x^{2} : x = 1, x = - \frac{1}{4}

x = 1, x = - \frac{1}{4}

Verify Solutions:

x = 1

False

, x = - \frac{1}{4}

True

The solution is

x = - \frac{1}{4}

- x + 2 x - 1 = 0

2 x + 8 + x + 5 = 7

2 = 2 π \cdot \frac{x}{32}

\frac{2 x ^{2} + 1}{x ^{2} + 1} = 0

2 x x - 13 x + 13 x + 10 = 0