Solve x^3 + 30 = 3

Step by step

The question

Question: solve x³ + 30 = 3.

x³ means x times x times x.

We want just x.

1 Remove the + 30

We want x³ by itself.

The + 30 is in the way.

To remove + 30, we take away 30.

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

+ 30 and − 30 make zero.

Cross them out.

Now we have x³ = −27.

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 −27.

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

−3 times −3 times −3 is −27.

So x = −3.

Careful!

With squares, a negative has no root.

With cubes it does: the answer is negative.

3 Check

Let's check: −3 times −3 times −3 is −27.

Plus 30 is 3.

The same as the right side.

So the answer is right!

Let's look back.

First: remove the + 30.

Then: cube root of both sides.

Last: check.