Question

Solve the equation -4x^3=32

Answer 1

`-4x^3= 32\\\\\implies x^3 = -\frac{32}4\\\\\implies x^3 = -8\\\\\implies x^3 +8 = 0\\\\\implies x^3 +2^3 =0\\\\\implies (x+2)(x^2 -2x +2^2)=0\\\\\implies (x+2)(x^2 -2x +4) = 0\\\\\implies x +2 =0~~~\text{or} ~~~~x^2 -2x +4 = 0\\ \\\implies x = -2 ~~~~~~\text{or} ~~~~ x= (2 \pm√(-12))/(2)=\frac{2 \pm i√(12)}2}=(2\pm2i\sqrt3)/(2)=1\pm i\sqrt 3\\\\\text{Hence,}~ x = -2,~~ x = 1+i\sqrt 3,~~~ x= 1-i\sqrt3`

Answer 2

-2

Explanation:

-4x^3 = 32

x^3 = -8

take the cube root of both sides.

x = -2