1/11*x=1

Solution for 1/11*x=1 equation:

1/11*x=1

We move all terms to the left:

1/11*x-(1)=0


Domain of the equation: 11*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-1*11*x+1=0

Wy multiply elements

-11x*x+1=0

Wy multiply elements

-11x^2+1=0

a = -11; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-11)·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{11}}{2*-11}=\frac{0-2\sqrt{11}}{-22}
=-\frac{2\sqrt{11}}{-22}
=-\frac{\sqrt{11}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{11}}{2*-11}=\frac{0+2\sqrt{11}}{-22}
=\frac{2\sqrt{11}}{-22}
=\frac{\sqrt{11}}{-11}
$