Solve 3x^3 = -24

Step by step

The question

Question: solve 3x³ = −24.

x³ means x times x times x.

We want just x.

1 Remove the 3

3x³ means 3 times x³.

We want just x³.

To remove times 3, we divide by 3.

We do it on both sides, so they stay equal.

3 divided by 3 is 1.

So just x³ is left.

−24 divided by 3 is −8.

Now we have x³ = −8.

2 Cube root of both sides

The cube root asks: which number, times itself three times, makes this?

The cubes: 1 times 1 times 1 is 1.

2 times 2 times 2 is 8.

3 times 3 times 3 is 27.

x is the cube root of −8.

A negative number, times itself three times, stays negative: minus times minus is plus, times minus again is minus.

−2 times −2 times −2 is −8.

So x = −2.

Careful!

With squares, a negative has no root.

With cubes it does: the answer is negative.

3 Check

Let's check: −2 times −2 times −2 is −8.

3 times −8 is −24.

The same as the right side.

So the answer is right!

Let's look back.

First: remove the 3.

Then: cube root of both sides.

Last: check.