What is the answer to sqrt(x)=5-sqrt(x*5) ?

The answer to sqrt(x)=5-sqrt(x*5) is x=(25(3-sqrt(5)))/8

Solve for x: sqrt(x)=5-sqrt(x*5)

The solution is x=(25(3-sqrt(5)))/8

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x = 5 - x \cdot 5

x = \frac{25 ( 3 - 5 )}{8}

Decimal Notation

x = 2.38728 \dots

Solution steps

x = 5 - x \cdot 5

Remove square roots

16 x^{2} + 200 x + 625 = 500 x

Solve

16 x^{2} + 200 x + 625 = 500 x : x = \frac{25 ( 3 + 5 )}{8}, x = \frac{25 ( 3 - 5 )}{8}

x = \frac{25 ( 3 + 5 )}{8}, x = \frac{25 ( 3 - 5 )}{8}

Verify Solutions:

x = \frac{25 ( 3 + 5 )}{8}

False

, x = \frac{25 ( 3 - 5 )}{8}

True

The solution is

x = \frac{25 ( 3 - 5 )}{8}

x^{\frac{2}{3}} = 2

x^{\frac{1}{2}} - 2 x + 4 = 0

x^{2} = x

x + 3 = - 6

\frac{( x + 3 )}{( x - 2 )} = \frac{( 3 x - 5 )}{( 3 x - 13 )}

What is the answer to sqrt(x)=5-sqrt(x*5) ?
The answer to sqrt(x)=5-sqrt(x*5) is x=(25(3-sqrt(5)))/8
Solve for x: sqrt(x)=5-sqrt(x*5)
The solution is x=(25(3-sqrt(5)))/8