<s>[INST] $3x^3 = 24$ quadratic equation Completing the square I know by factoring
$$x^3 - 8 = 0\\
x-2 = 0$$
that one of the solutions is 2.
but the other solutions is $1 ± i \sqrt 3$.
Can someone explain to me how to get that?
 [/INST] As David Mitra commented, one may factor using polynomial division:
$\frac {x^3 - 8} {x-2} = (x^2+2x+4)$
To solve this, we can quickly complete the square as follows:
Notice that we are setting $x^2 + 2x+4 = 0$
$(x+1)^2 + 3 = 0$
$(x+1)^2 = -3$
$x+1 = \pm i \sqrt{3}$
$x = -1 \pm i \sqrt{3}$ and we have our answer.  I find this slightly faster than using the quadratic formula.
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