Question

Which of the following sets represents the solution of the equation below?

Answer 1

Answer:

$x=\frac{-1+\sqrt{5}i}{3}$ or $x=\frac{-\sqrt{5}i-1}{3}$

Step-by-step explanation:

The given equation is

$-\frac{3}{2}x^2=x+1$

We multiply through by -2 to get;

$3x^2=-2x-2$

We rewrite in standard quadratic equation form to obtain;

$3x^2+2x+2=0$

The solution to this equation can be found using the formula;

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where $a=3,b=2,c=2$

We substitute these values to obtain;

$x=\frac{-2\pm\sqrt{2^2-4(3)(2)}}{2(3)}$

This implies that;

$x=\frac{-2\pm\sqrt{4-24}}{6}$

$x=\frac{-2\pm\sqrt{-20}}{6}$

$x=\frac{-2\pm2\sqrt{-5}}{6}$

$x=\frac{-1\pm\sqrt{5}i}{3}$

Hence the solution is;

$x=\frac{-1+\sqrt{5}i}{3}$ or $x=\frac{-\sqrt{5}i-1}{3}$