10^x=1/x

Solution for 10^x=1/x equation:

10^x=1/x

We move all terms to the left:

10^x-(1/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10^x-(+1/x)=0

We get rid of parentheses

10^x-1/x=0

We multiply all the terms by the denominator


10^x*x-1=0

Wy multiply elements

10x^2-1=0

a = 10; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·10·(-1)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*10}=\frac{0-2\sqrt{10}}{20}
=-\frac{2\sqrt{10}}{20}
=-\frac{\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*10}=\frac{0+2\sqrt{10}}{20}
=\frac{2\sqrt{10}}{20}
=\frac{\sqrt{10}}{10}
$