Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
Given equation:
[tex]2x^3+16=0[/tex]
To solve for the unknown variable x, apply arithmetic operations to isolate the variable.
Subtract 16 from both sides:
[tex]\implies 2x^3+16-16=0-16[/tex]
[tex]\implies 2x^3=-16[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2x^3}{2}=\dfrac{-16}{2}[/tex]
[tex]\implies x^3=-8[/tex]
Take the cube root of both sides:
[tex]\implies \sqrt[3]{x^3}=\sqrt[3]{-8}[/tex]
[tex]\implies x=-2[/tex]
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:
[tex]\begin{aligned}\implies (-2)^3 &= -2 \cdot -2 \cdot -2\\ & = 4 \cdot -2\\& = -8\end{aligned}[/tex]
So if -8 is cube rooted, the result is -2.
