Finding the Real Part of a Complex Function's Root

Consider the complex function defined by:

$$ f(z) = z^2 + (1 - i)z + (1 + i) $$

where $$ z $$ is a complex number in the form $$ z = a + bi $$, with $$ a $$ and $$ b $$ being real numbers. To find the value of $$ z $$ such that $$ f(z) = 0 $$, express $$ z $$ in the standard form $$ a + bi $$ and calculate the real part $$ a $$ of the solution. Provide your answer as a decimal.