Solution to basic Mensa Algebra Problem

    Find all values of x that satisfy the equation:

x ² +  x ³ = 36 

Factor after re-arranging order:

(x + 3) (x² -  4x + 12)  = 0

(x + 3)  = 0,   

so x = -3  is one REAL root

For the quadratic part of the equation we can use the quadratic formula:

x = -b + Ö {b² - 4ac}/ 2a

Where: a = 1, b = - 4, c = 12

Working:

x = - (- 4) + Ö {4² - 4(12)}/ 2

x =  4 + Ö {16 - (48)}/ 2

x =  4 + Ö {- 32} / 2

x =  4 + iÖ {16 (2)} / 2

x =  4 + 4iÖ (2)) / 2

x = 2 + 2iÖ 2) 

Yielding two imaginary roots:

x = 2 + 2iÖ 2 ,    x = 2 - 2iÖ 2 

in addition to the single real root