x^2+4x+2^2=0.5

Solution for x^2+4x+2^2=0.5 equation:

x^2+4x+2^2=0.5

We move all terms to the left:

x^2+4x+2^2-(0.5)=0

We add all the numbers together, and all the variables

x^2+4x+3.5=0

a = 1; b = 4; c = +3.5;
Δ = b2-4ac
Δ = 42-4·1·3.5
Δ = 2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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