What is the answer to sqrt(x^2+5)=x+3 ?

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

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sqrt(x^2+5)=x+3

x^{2} + 5 = x + 3

x = - \frac{2}{3}

Decimal Notation

x = - 0.66666 \dots

Solution steps

x^{2} + 5 = x + 3

Square both sides:

x^{2} + 5 = x^{2} + 6 x + 9

x^{2} + 5 = x^{2} + 6 x + 9

Solve

x^{2} + 5 = x^{2} + 6 x + 9 : x = - \frac{2}{3}

x = - \frac{2}{3}

Verify Solutions:

x = - \frac{2}{3}

True

The solution is

x = - \frac{2}{3}

(6 x - 3)^{\frac{2}{3}} + 6 = 15

x^{\frac{4}{3}} = 81

x^{2} - 6 x = 13 x^{2} - 6 x - 36

y = 3 + y^{2} - 5

x^{2} = 4