Question

Solve the equation x³ = -125. Please show work.

Answer 1

The solution to the equation x³ = -125 is x = -5.

Step-by-step explanation:

To solve the equation x³ = -125, we can find the cube root of both sides to isolate x. The cube root of -125 is -5, as (-5)³ equals -125. Therefore, the solution to the equation is x = -5.

Now, let's go through the process of solving it more thoroughly. Start with the given equation: x³ = -125. To isolate x, take the cube root of both sides:
`\sqrt[(3)]{(x^(3) )} = \sqrt[3]{-125}`. This simplifies to x = -5, as the cube root of -125 is indeed -5.

In mathematical terms, when you have an equation in the form
`x^n` = a, taking the n-th root of both sides will yield the solution. In this case, since we have x³ = -125, taking the cube root gives x = -5. This process relies on the fundamental property of exponents and roots, providing a straightforward method to find the solution to cubic equations.