Question 23418
Start by letting x = the first negative even integer.  The next consecutive negative even integer is x+2. 
From the problem description, you can write:

{{{x^2 + (x+2)^2 = 100}}} Simplify and solve for x.
{{{x^2 + x^2 + 4x + 4 = 100}}} Subtract 100 from both sides of the equation.
{{{2x^2 + 4x - 96 = 0}}} Factor out a 2.
{{{2(x^2 + 2x - 48) = 0}}} Factor the parentheses.
{{{2(x - 6)(x + 8) = 0}}} Apply the zero product principle.
{{{x - 6 = 0}}} and/or {{{x + 8 = 0}}}
If {{{x - 6 = 0}}} then {{{x = 6}}} Discard this solution...you want negative integers.
If {{{x + 8 = 0}}} then {{{x = -8}}} This solution is valid and {{{x+2 = -8+2}}} = {{{-6}}}

The two consecutive negative even integers are:

-8 and -6

Check:

{{{(-8)^2 + (-6)^2 = 64 + 36}}} = {{{100}}}