Question

Find the roots of... X^2+10X+34

Answer 1

$x^{2} +10x+34=0\\ \\ \Delta=10^2-4.1.34=100-136=-36\\ \\ \boxed{x=\frac{-10\pm\sqrt{-36}}{2}=\frac{-10 \pm6i}{2}=-5\pm3i}$

Answer 2

$x^2+10x+34=0\\\\x^2+2\cdotx\cdot5+5^2+9=0\\\\(x+5)^2=-9\ \ \ \Rightarrow\ \ \ no\ real\ solution\\\\(x+5)^2=9\cdot i^2\ \ \ \Rightarrow\ \ \ ( x+5=3i\ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ x+5=-3i)\\\\x_1=-5+3i,\ \ \ \ \ x_2=-5-3i\ \ \ \rightarrow\ \ \ two\ complex\ numbers\ solution$