Answer:
[tex] x = -\dfrac{1}{8} + \dfrac{\sqrt{1095}}{24}i [/tex] or [tex] x = -\dfrac{1}{8} - \dfrac{\sqrt{1095}}{24}i [/tex]
Step-by-step explanation:
24x² + 6x + 46 = 0
Divide both sides by t he GCF, 2:
12x² + 3x + 23 = 0
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
We have a = 12; b = 3; c = 23.
[tex] x = \dfrac{-3 \pm \sqrt{3^2 - 4(12)(23)}}{2(12)} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{9 - 1104}}{24} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{-1095}}{24} [/tex]
[tex] x = \dfrac{-3 \pm i\sqrt{1095}}{24} [/tex]
[tex] x = -\dfrac{1}{8} + \dfrac{\sqrt{1095}}{24}i [/tex] or [tex] x = -\dfrac{1}{8} - \dfrac{\sqrt{1095}}{24}i [/tex]
