Step by step
The question
Question: solve x³ − 4 = 60.
x3 − 4 = 60
x³ means x times x times x.
We want just x.
x³ = x × x × x
1 Remove the − 4
We want x³ by itself.
The − 4 is in the way.
To remove − 4, we add 4.
We do it on both sides, so they stay equal.
x3 − 4 + 4 = 60 + 4
− 4 and + 4 make zero.
Cross them out.
Now we have x³ = 64.
x3 = 64
2 Cube root of both sides
The cube root asks: which number, times itself three times, makes this?
∛27 = ? → ? × ? × ? = 27
The cubes: 1 times 1 times 1 is 1.
2 times 2 times 2 is 8.
3 times 3 times 3 is 27.
4 times 4 times 4 is 64.
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64
x is the cube root of 64.
x = 3√64
4 times 4 times 4 is 64.
So x = 4.
x = 4
Careful!
A cube has one answer, not two.
Minus 4, cubed, is minus 64.
Not like x² = 49.
Careful: not x = 4 or x = −4 ✗
3 Check
Let's check: 4 times 4 times 4 is 64.
4 × 4 × 4 = 64
Minus 4 is 60.
The same as the right side.
So the answer is right!
64 − 4 = 60
Let's look back.
First: remove the − 4.
Then: cube root of both sides.
Last: check.
Answer
Careful: not x = 4 or x = −4 ✗