Choose a method: 4x^2 - 9 = 0 Step by Step

Step by step

The question

Question: choose a method and solve 4x² − 9 = 0.

4x² − 9 = 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 − 9, we add 9 on both sides.

4x² − 9 + 9 = 0 + 9

0 + 9 = 9.

Now we have 4x² = 9.

4x² = 9

To remove times 4, we divide both sides by 4.

4x²4 = 94

9 divided by 4 is 9/4.

x² = 94

3 Square root of both sides

x squared is 9/4.

So x is the square root of 9/4, or minus it.

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

x² = k → x = √k or x = −√k

The square root of a fraction is the root of the top over the root of the bottom.

3 times 3 is 9, and 2 times 2 is 4.

√94 = √9√4 = 32

So x = 3/2 or x = −3/2.

x = 32 or x = −32

Careful!

Many people write only x = 3/2.

They lose the minus answer.

Careful: not only x = 32 ✗

4 Check

Let's check: put x = 3/2 into the left side.

x = 32: 4(32)² − 9 = 9 − 9 = 0

We get 0, the same as the right side.

It works!

Now put x = −3/2 into the left side.

x = −32: 4(−32)² − 9 = 9 − 9 = 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