What is the answer to sqrt(x+2\sqrt{x)-1}=2 ?

The answer to sqrt(x+2\sqrt{x)-1}=2 is x=7-2sqrt(6)

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sqrt(x+2\sqrt{x)-1}=2

x + 2 x - 1 = 2

x = 7 - 26

Decimal Notation

x = 2.10102 \dots

Solution steps

x + 2 x - 1 = 2

Remove square roots

4 x = x^{2} - 10 x + 25

Solve

4 x = x^{2} - 10 x + 25 : x = 7 + 26, x = 7 - 26

x = 7 + 26, x = 7 - 26

Verify Solutions:

x = 7 + 26

False

, x = 7 - 26

True

The solution is

x = 7 - 26

16 + x + 18 = 121

- 9 x + 10 = 3 x^{0.2}

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

\frac{2 x - 1 + ( 4 x + 9 )}{( 2 x - 1 )} = 0

2 - 14 = \frac{288}{x}

What is the answer to sqrt(x+2\sqrt{x)-1}=2 ?
The answer to sqrt(x+2\sqrt{x)-1}=2 is x=7-2sqrt(6)
Solve for x: sqrt(x+2\sqrt{x)-1}=2
The solution is x=7-2sqrt(6)