How do you solve x(x^2 + 16) = 0?

Apr 27, 2018

$x$ = 0

Explanation:

In multiplication, the only way to have $0$ as a product is to multiply a number(s) by at least one $0$. Using this property of multiplication, we know that at least one of the terms is equal to $0$:

$x$ = 0 | ${x}^{2}$ + 16 = 0

To solve for the second term, first subtract $16$ from both sides of the equation, giving us:

${x}^{2}$ = -16

However, there is no real number that can be squared to equal a number lower than $0$, so there is no real solution for the second term.

Apr 27, 2018

Shown below

Explanation:

We know if $a b = 0$

Then $a = 0$ or $b = 0$

color(red)(=> x = 0

$\implies {x}^{2} + 16 = 0$

$\implies {x}^{2} = - 16$

color(blue)(=> x = pm 4i

If $x \in \mathbb{R} \to x = \left\{0\right\}$

if $x \in \mathbb{C} \to x = \left\{0 , 4 i , - 4 i\right\}$