What is the answer to sqrt(x^2+5)=2x+1 ?

The answer to sqrt(x^2+5)=2x+1 is x= 2/3

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sqrt(x^2+5)=2x+1

x^{2} + 5 = 2 x + 1

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

x^{2} + 5 = 2 x + 1

Square both sides:

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

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

Solve

x^{2} + 5 = 4 x^{2} + 4 x + 1 : x = \frac{2}{3}, x = - 2

x = \frac{2}{3}, x = - 2

Verify Solutions:

x = \frac{2}{3}

True

, x = - 2

False

The solution is

x = \frac{2}{3}

4 x^{2} + 4 x + 1 = 3 - 4 x

x - 2 x + 4 + 5 = x + 3

3 \cdot 2 x^{0.36} = 0

\frac{4}{x ^{2} + 2 x - 3} = 0

6.745 = 0.6927 (x^{0.4992})

What is the answer to sqrt(x^2+5)=2x+1 ?
The answer to sqrt(x^2+5)=2x+1 is x= 2/3
Solve for x: sqrt(x^2+5)=2x+1
The solution is x= 2/3