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=(-10\pm√(-36))/(2)=(-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`