Step by step
The question
Question: solve x³ + 5 = 13.
x3 + 5 = 13
x³ means x times x times x.
We want just x.
x³ = x × x × x
1 Remove the + 5
We want x³ by itself.
The + 5 is in the way.
To remove + 5, we take away 5.
We do it on both sides, so they stay equal.
x3 + 5 − 5 = 13 − 5
+ 5 and − 5 make zero.
Cross them out.
Now we have x³ = 8.
x3 = 8
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 8.
x = 3√8
2 times 2 times 2 is 8.
So x = 2.
x = 2
Careful!
A cube has one answer, not two.
Minus 2, cubed, is minus 8.
Not like x² = 49.
Careful: not x = 2 or x = −2 ✗
3 Check
Let's check: 2 times 2 times 2 is 8.
2 × 2 × 2 = 8
Plus 5 is 13.
The same as the right side.
So the answer is right!
8 + 5 = 13
Let's look back.
First: remove the + 5.
Then: cube root of both sides.
Last: check.
Answer
Careful: not x = 2 or x = −2 ✗