Step by step
The question
Question: solve 2x³ = 54.
2x3 = 54
x³ means x times x times x.
We want just x.
x³ = x × x × x
1 Remove the 2
2x³ means 2 times x³.
We want just x³.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x³ is left.
54 divided by 2 is 27.
Now we have x³ = 27.
x3 = 27
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.
1³ = 1, 2³ = 8, 3³ = 27
x is the cube root of 27.
x = 3√27
3 times 3 times 3 is 27.
So x = 3.
x = 3
Careful!
A cube has one answer, not two.
Minus 3, cubed, is minus 27.
Not like x² = 49.
Careful: not x = 3 or x = −3 ✗
3 Check
Let's check: 3 times 3 times 3 is 27.
3 × 3 × 3 = 27
2 times 27 is 54.
The same as the right side.
So the answer is right!
2 × 27 = 54
Let's look back.
First: remove the 2.
Then: cube root of both sides.
Last: check.
Answer
Careful: not x = 3 or x = −3 ✗