Choose a method: 3x^2 - 27 = 0 Step by Step

Step by step

The question

Question: choose a method and solve 3x² − 27 = 0.

3x² − 27 = 0

1 Choose the method

There is no x term.

So we can get x² alone and take the square root.

That is the quickest way.

So: square root.

1. no x term, or ( )² = k? ✓ square root

2 Get x² alone

There is no x term, so we get x² by itself.

To remove the − 27, we add 27 on both sides.

3x² − 27 + 27 = 0 + 27

0 + 27 = 27.

Now we have 3x² = 27.

3x² = 27

To remove times 3, we divide both sides by 3.

3x²3 = 273

27 divided by 3 is 9.

x² = 9

3 Square root of both sides

x squared is 9.

So x is the square root of 9, or minus it.

Minus times minus is plus, so the negative one works too.

x² = k → x = √k or x = −√k

3 × 3 = 9, (−3) × (−3) = 9

3 times 3 is 9.

So x = 3 or x = −3.

x = 3 or x = −3

Careful!

Many people write only x = 3.

They lose the minus answer.

Careful: not only x = 3 ✗

4 Check

Let's check: put x = 3 into the left side.

x = 3: 3(3)² − 27 = 27 − 27 = 0

We get 0, the same as the right side.

It works!

Now put x = −3 into the left side.

x = −3: 3(−3)² − 27 = 27 − 27 = 0

We get 0 again, the same as the right side.

So both answers are right!

Let's look back.

First: choose the method.

Then: get x² alone.

Then: square root of both sides.

Last: check.

Answer