What is the solution of $\sqrt[3]{x+8}=-4$?

Cube both sides of the equation: ( 3 x + 8 ​ ) 3 = ( − 4 ) 3 , which simplifies to x + 8 = − 64 .
Subtract 8 from both sides: x = − 64 − 8 .
Calculate the value of x: x = − 72 .
The solution to the equation is − 72 ​ .

Explanation

Understanding the problem We are given the equation 3 x + 8 ​ = − 4 . Our goal is to find the value of x that satisfies this equation. We will start by cubing both sides of the equation to eliminate the cube root.

Cubing both sides Cube both sides of the equation: ( 3 x + 8 ​ ) 3 = ( − 4 ) 3 . This simplifies to x + 8 = − 64 .

Isolating x Now, we solve for x by subtracting 8 from both sides of the equation: x = − 64 − 8 .

Calculating x Calculating the value of x , we get x = − 72 .

Final Answer Therefore, the solution to the equation 3 x + 8 ​ = − 4 is x = − 72 .


Examples
Imagine you are designing a cubic container, and you know that the volume inside needs to relate to a certain number. This problem demonstrates how to work backwards from a cube root to find the original dimension, which is useful in engineering and design when dealing with volumes and dimensions.

Answered by GinnyAnswer | 2025-07-03

To solve 3 x + 8 ​ = − 4 , we first cube both sides to get x + 8 = − 64 . Then, by subtracting 8, we find that x = − 72 . Thus, the solution is x = − 72 .
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Answered by Anonymous | 2025-07-04