(1/(200x))+x=1

Solution for (1/(200x))+x=1 equation:

(1/(200x))+x=1

We move all terms to the left:

(1/(200x))+x-(1)=0


Domain of the equation: 200x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/200x)+x-1=0

We add all the numbers together, and all the variables

x+(+1/200x)-1=0

We get rid of parentheses

x+1/200x-1=0

We multiply all the terms by the denominator


x*200x-1*200x+1=0

Wy multiply elements

200x^2-200x+1=0

a = 200; b = -200; c = +1;
Δ = b2-4ac
Δ = -2002-4·200·1
Δ = 39200
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:

$\sqrt{\Delta}=\sqrt{39200}=\sqrt{19600*2}=\sqrt{19600}*\sqrt{2}=140\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-140\sqrt{2}}{2*200}=\frac{200-140\sqrt{2}}{400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+140\sqrt{2}}{2*200}=\frac{200+140\sqrt{2}}{400}
$