Reciprocal value

How do I calculate a number x that is 9 greater than its reciprocal (1/x)?

Correct answer:

x₁ =  9.10977
x₂ =  -0.10977

Step-by-step explanation:

$$\begin{gathered} x=9+1\mathrm{/}x \\ {x}^2=9x+1 \\ {x}^2=9x+1 \\ {x}^2-9x-1=0 \\ a=1;b=-9;c=-1 \\ D=b^2-4ac=9^2-4\cdot 1\cdot (-1)=85 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{9\pm \sqrt{85}}{2}} \\ {x}_{1,2}=4.5\pm 4.60977222865 \\ {x}_1=9.10977222865=9.10977 \\ {x}_2=-0.109772228646 \\ \text{ Factored form of the equation: } \\ (x-9.10977222865)(x+0.109772228646)=0 \end{gathered}$$

Our quadratic equation calculator calculates it.

$x_2=(-0.1098)=-0.10977$

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