ANSWER
\(x = - 2 \pm i\)
EXPLANATION
We use the method of completing the squares.
The equation is
\(3 {x}^{2} = - 12x - 15\)
We rewrite the above equation to obtain;
\(3 {x}^{2} + 12x = - 15\)
We divide through by 3 to obtain;
\({x}^{2} + 4x = - 5\)
We add half the coefficient of
\(x\)
to both sides of the equation to get,
\({x}^{2} + 4x + {2}^{2} = - 5 + {2}^{2}\)
The right hand side is now a perfect square.
\({(x + 2)}^{2} = - 1\)
We now take square root of both sides to get;
\(x + 2 = \pm \sqrt{ - 1}\)
We add -2 to both sides,
\(x = - 2 \pm \sqrt{ - 1}\)
We simplify to obtain,
\(x = - 2 \pm i\)
