Question

Whats the answer for -2x^2-28x-102=0

Answer 1

NO REAL SOLUTIONS

complex solutions: x = -7 ± i√2

Explanation:

`-2x^2-28x-102=0\\{}\qquad\qquad^(/(-2))\qquad\ \ ^(/(-2))\\x^2+14+51=0\quad\implies\quad a=1\,,\ b=14\,,\ c=51\\\\\\x=(-b\pm√(b^2-4ac))/(2a)=(-14\pm√(14^2-4\cdot1\cdot51))/(2\cdot1)=(-14\pm√(196-204))/(2)`

`x=(-14\pm√(-8))/(2)` means NO REAL SOLUTIONS (as there is no real √[-8])

However in complex numbers we have:
`x=(-14\pm√(-8))/(2)=(-14\pm2√(-2))/(2)=(2(-7\pm√(-2)))/(2)=-7\pm√(-2)\\\\\\x_1=-7+i\sqrt2\ ,\qquad x_2=-7-i\sqrt2`