Answer:
[tex]x= \dfrac 12 \left( -3 +i5\sqrt 3\right)\\\\x= \dfrac 12 \left( -3 -i5\sqrt 3\right)[/tex]
Step-by-step explanation:
[tex]~~~~~~x^2 +3x +21 = 0\\\\\implies x^2 +3x = -21\\\\\implies x^2 + 2\cdot \dfrac 32 \cdot x + \left( \dfrac 32 \right)^2 = -21 + \left( \dfrac 32 \right)^2\\\\\implies \left(x + \dfrac 32 \right)^2 = -21+\dfrac 94\\\\\implies \left(x + \dfrac 32 \right)^2 = -\dfrac{75}4\\\\\implies x+ \dfrac 32 = \pm\sqrt{-\dfrac{75}4 \right)\\\\\implies x + \dfrac 32 = \pm i \dfrac{5\sqrt 3}{2}\\\\\implies x = -\dfrac 32 \pm i \dfrac {5\sqrt 3}2\\\\\implies x = \dfrac 12 \left( -3 \pm i5\sqrt 3\right)[/tex]
