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

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

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3-2x=sqrt(2x+3)

3 - 2 x = 2 x + 3

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

3 - 2 x = 2 x + 3

Square both sides:

9 - 12 x + 4 x^{2} = 2 x + 3

9 - 12 x + 4 x^{2} = 2 x + 3

Solve

9 - 12 x + 4 x^{2} = 2 x + 3 : x = 3, x = \frac{1}{2}

x = 3, x = \frac{1}{2}

Verify Solutions:

x = 3

False

, x = \frac{1}{2}

True

The solution is

x = \frac{1}{2}

6 = x^{2} + 3 - x

x = 9 x + 4

x^{2} - x - 9 = x + 3

x^{2} - x - 9 = x + 5