What is the answer to sqrt(4x+1)+x=sqrt(5) ?

The answer to sqrt(4x+1)+x=sqrt(5) is x=sqrt(5)+2-sqrt(5+4\sqrt{5)}

Solve for x: sqrt(4x+1)+x=sqrt(5)

The solution is x=sqrt(5)+2-sqrt(5+4\sqrt{5)}

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4 x + 1 + x = 5

x = 5 + 2 - 5 + 45

Decimal Notation

x = 0.50186 \dots

Solution steps

4 x + 1 + x = 5

Remove square roots

4 x + 1 = 5 - 25 x + x^{2}

Solve

4 x + 1 = 5 - 25 x + x^{2} : x = 5 + 2 + 5 + 45, x = 5 + 2 - 5 + 45

x = 5 + 2 + 5 + 45, x = 5 + 2 - 5 + 45

Verify Solutions:

x = 5 + 2 + 5 + 45

False

, x = 5 + 2 - 5 + 45

True

The solution is

x = 5 + 2 - 5 + 45

0 = x^{2} - 9

x^{\frac{3}{4}} = - 8

2 x + 9 = 21

x^{2} + 9 = 5

4 x^{2} - 5 x + 50 = 2 x

What is the answer to sqrt(4x+1)+x=sqrt(5) ?
The answer to sqrt(4x+1)+x=sqrt(5) is x=sqrt(5)+2-sqrt(5+4\sqrt{5)}
Solve for x: sqrt(4x+1)+x=sqrt(5)
The solution is x=sqrt(5)+2-sqrt(5+4\sqrt{5)}