What is the answer to 2x+sqrt(6x+1)=3 ?

The answer to 2x+sqrt(6x+1)=3 is x= 1/2

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2x+sqrt(6x+1)=3

2 x + 6 x + 1 = 3

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

2 x + 6 x + 1 = 3

Remove square roots

6 x + 1 = 9 - 12 x + 4 x^{2}

Solve

6 x + 1 = 9 - 12 x + 4 x^{2} : x = 4, x = \frac{1}{2}

x = 4, x = \frac{1}{2}

Verify Solutions:

x = 4

False

, x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

4 x + 1 = 5

4 x + 1 = 3

5 x + 49 + 7 = x

32 - 4 x - x = 0

55 - 4 x - 2 7 - x = 3