Solve for x:

First, to undo the cubed root, we'd better cube both sides. In other words, raise both sides to the third power.

x – 1 = 512

In a stunning algebraic move, we'll add 1 to both sides to get the final answer.

x – 1 = 512
x = 513

Solve for x: 

To get things started, we must square both sides.

x³ – 8 = 9

Adding 8 to both sides moves us closer to getting x all by itself.

x³ – 8 = 9
x³ = 17

While it certainly isn't going to be pretty, we must take the cubed root of 17 to solve. Our answer is given here as an exact answer and as a decimal rounded to two decimal places. Who doesn't like a bonus solution?

x³ = 17

x ≈ 2.57

Solve for x:

We have to try to get rid of at least one square root. To begin, we square both sides.

The second step is to subtract x from both sides.

Next, we can subtract 4 from both sides.

To undo the multiplication, we can divide both sides by 4.

Finally, if we square both sides, we'll have a pretty nice little solution.

Solve for x: 

Step 1: Take a deep breath.

Now that the breathing portion of this example is out of the way, let's start by cubing both sides.

Next, we can divide both sides by x, but first make sure we note that x = 0 is a solution.

x(x)³ = -8x
(x)³ = -8

Finally, taking the cubed root of both sides allows us to find a solution.

(x)³ = -8

x = -2

But wait just a second, don't forget that 0 is a solution too. Careful, soldier.

x = 0, -2