1/2k-1/2k+1=-k

Solution for 1/2k-1/2k+1=-k equation:

1/2k-1/2k+1=-k

We move all terms to the left:

1/2k-1/2k+1-(-k)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We add all the numbers together, and all the variables

1/2k-1/2k-(-1k)+1=0

We get rid of parentheses

1/2k-1/2k+1k+1=0

We multiply all the terms by the denominator


1k*2k+1*2k+1-1=0

We add all the numbers together, and all the variables

1k*2k+1*2k=0

Wy multiply elements

2k^2+2k=0

a = 2; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·2·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*2}=\frac{-4}{4}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*2}=\frac{0}{4}
=0
$