k^2=1000

Solution for k^2=1000 equation:

k^2=1000

We move all terms to the left:

k^2-(1000)=0

a = 1; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·1·(-1000)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*1}=\frac{0-20\sqrt{10}}{2}
=-\frac{20\sqrt{10}}{2}
=-10\sqrt{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*1}=\frac{0+20\sqrt{10}}{2}
=\frac{20\sqrt{10}}{2}
=10\sqrt{10}
$