Question

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

Answer 1

x = -2

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

Answer 2

`x=-2`

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