Question

Solve 2x^2 +16x+50=0

Answer 1

$2x^2 +16x+50=0\ \ \ \ \ |:2\\\\x^2+8x+25=0\\\\x^2+2\cdot x\cdot4+25=0\ \ \ \ |+4^2\\\\\underbrace{x^2+2\cdot x\cdot4+4^2}_{(a+b)^2=a^2+2ab+b^2}+25=4^2\ \ \ \ \ |-25\\\\(x+4)^2=16-25\\\\(x+4)^2=-9 < 0-NO\ REAL\ SOLUTION$

$COMPLEX\ SOLUTIONS\\\\(x+4)^2=-9\to x+4=\pm\sqrt{-9}\\\\x+4=-3i\ \vee\ x+4=3i\ \ \ \ |-4\\\\x=-4-3i\ \vee\ x=-4+3i$