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

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

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

2 x - 2 x - 3 = x + 2

x = 3 + 2

Decimal Notation

x = 4.41421 \dots

Solution steps

2 x - 2 x - 3 = x + 2

Remove square roots

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

Solve

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

x = 3 + 2, x = 3 - 2

Verify Solutions:

x = 3 + 2

True

, x = 3 - 2

False

The solution is

x = 3 + 2

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

8 x^{\frac{3}{2}} - 40 = 0

\frac{1}{5} = x^{\frac{1}{3}}

x + 32 - x - 8 = 4

x^{2} - 698.88 = x - 23.52

What is the answer to 2x-sqrt(2x-3)=x+2 ?
The answer to 2x-sqrt(2x-3)=x+2 is x=3+sqrt(2)
Solve for x: 2x-sqrt(2x-3)=x+2
The solution is x=3+sqrt(2)