K(x)=-1/2x-2

Solution for K(x)=-1/2x-2 equation:

(K)=-1/2K-2

We move all terms to the left:

(K)-(-1/2K-2)=0


Domain of the equation: 2K-2)!=0

K∈R


We get rid of parentheses

K+1/2K+2=0

We multiply all the terms by the denominator


K*2K+2*2K+1=0

Wy multiply elements

2K^2+4K+1=0

a = 2; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·2·1
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{2}}{2*2}=\frac{-4-2\sqrt{2}}{4}
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{2}}{2*2}=\frac{-4+2\sqrt{2}}{4}
$