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

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

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

We move all terms to the left:

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

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

k^2*2-1k-1=0

Wy multiply elements

2k^2-1k-1=0

a = 2; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·2·(-1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*2}=\frac{-2}{4}
=-1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*2}=\frac{4}{4}
=1
$