Answer: [tex]x =\dfrac{\fbox{-3}+i \sqrt{} \fbox{11} }{\fbox{10}}\: \: \: \: or\: \: \: \: x =\dfrac{\fbox{-3}-i\sqrt{} \fbox{11} }{\fbox{10}}[/tex]
Step-by-step explanation:
Find the discriminant.
-5x² - 3x - 1 = 0
D = b² - 4a · c
a = - 5
b = - 3
c = - 1
[tex]D=(-3)^{2} -4 \cdot (-5) \cdot (-1) = -11 < 0\\\\D=-11=- 1 \cdot 11 = i^{2} \cdot 11\\\\\sqrt{D} =\sqrt{i^{2} \cdot 11} =i\sqrt{11}\\\\ x_{1} =\dfrac{3+i\sqrt{11} }{2 \cdot (- 5)} =\dfrac{3+i\sqrt{11} }{-10}=\dfrac{-3-i\sqrt{11} }{10}\\\\x_{2} =\dfrac{3-i\sqrt{11} }{2 \cdot (- 5)} =\dfrac{3-i\sqrt{11} }{-10}=\dfrac{-3+i\sqrt{11} }{10}[/tex]
