Question

Could someone explain why the value of x is (-2).​

Answer 1

Answer:

$x=-2$

Step-by-step explanation:

Given equation:

$2x^3+16=0$

To solve for the unknown variable x, apply arithmetic operations to isolate the variable.

Subtract 16 from both sides:

$\implies 2x^3+16-16=0-16$

$\implies 2x^3=-16$

Divide both sides by 2:

$\implies \dfrac{2x^3}{2}=\dfrac{-16}{2}$

$\implies x^3=-8$

Take the cube root of both sides:

$\implies \sqrt[3]{x^3}=\sqrt[3]{-8}$

$\implies x=-2$

When taking the cube root of a negative number, the result will be negative.  To understand why, examine what happens when we cube a negative number.

When a number is cubed, it is multiplied by itself, then by itself again.

When multiplying a negative number by another negative number, the result is always positive.

When multiplying a positive number by a negative number, the result is always negative.

Therefore:

$\begin{aligned}\implies (-2)^3 &= -2 \cdot -2 \cdot -2\\ & = 4 \cdot -2\\& = -8\end{aligned}$

So if -8 is cube rooted, the result is -2.

Answer 2

Answer:

x = -2

Step-by-step explanation:

2x^3 +16 = 0

We are solving for x

Subtract 16 from each side

2x^3 +16- 16 = 0-16

2x^3 = -16

Divide each side by 2

(2x^3 ) /2 = -16/2

x^3 = -8

Take the cube root of each side

$\sqrt[3]{x^3} = \sqrt[3]{-8}$

x = -2