[tex]-2x^2-16x-44=0\ \ \ |divide\ both\ sides\ by\ (-2)\\\\x^2+8x+11=0\ \ \ |subtract\ 11\ from\ both\ sides\\\\x^2+2x\cdot4=-11\ \ \ \ |add\ 4^2\ to\ both\ sides\\\\x^2+2x\cdot4+4^2=-11+4^2\ \ \ \ |use\ a^2+2ab+b^2=(a+b)^2\\\\(x+4)^2=-11+16\\\\(x+4)^2=5\iff x+4=\pm\sqrt5\ \ \ |subtract\ 4\ from\ both\ sides\\\\\boxed{x=-4-\sqrt5\ or\ x=-4+\sqrt5}[/tex]
