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

The answer to sqrt(x^2-\sqrt{2x+1)}=2-x is x= 3/2

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

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

x = \frac{3}{2}

Decimal Notation

x = 1.5

Solution steps

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

Remove square roots

2 x + 1 = 16 - 32 x + 16 x^{2}

Solve

2 x + 1 = 16 - 32 x + 16 x^{2} : x = \frac{3}{2}, x = \frac{5}{8}

x = \frac{3}{2}, x = \frac{5}{8}

Verify Solutions:

x = \frac{3}{2}

True

, x = \frac{5}{8}

False

The solution is

x = \frac{3}{2}

5 + 3 x = 8

6 x + 1 - 8 = 3

y, x = y - 1

3 x + 7 = x - 1

x - 2 = x - 8

What is the answer to sqrt(x^2-\sqrt{2x+1)}=2-x ?
The answer to sqrt(x^2-\sqrt{2x+1)}=2-x is x= 3/2
Solve for x: sqrt(x^2-\sqrt{2x+1)}=2-x
The solution is x= 3/2