Choose a method: (x - 3)^2 = 16 Step by Step

Step by step

The question

Question: choose a method and solve (x − 3)² = 16.

(x − 3)² = 16

1 Choose the method

It is already a bracket squared.

So we take the square root.

That is the quickest way.

So: square root.

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

2 Square root of both sides

Something squared is 16.

So that something is the square root of 16, or minus it.

Both work, because minus times minus is plus.

( )² = k → ( ) = √k or −√k

The square root of 16 is 4, because 4 times 4 is 16.

x − 3 = 4 or x − 3 = −4

Careful!

Many people write only x − 3 = 4.

They lose the minus answer.

Careful: not only x − 3 = 4 ✗

3 Get x alone

To remove the − 3, we add 3 on both sides.

We do it in both equations.

x = 4 + 3 or x = −4 + 3

So x = 7 or x = −1.

x = 7 or x = −1

4 Check

Let's check: put x = 7 into the left side.

x = 7: 7² − 6(7) + 9 = 49 − 42 + 9 = 16

We get 16, the same as the right side.

It works!

Now put x = −1 into the left side.

x = −1: (−1)² − 6(−1) + 9 = 1 + 6 + 9 = 16

We get 16 again, the same as the right side.

So both answers are right!

Let's look back.

First: choose the method.

Then: square root of both sides.

Then: get x alone.

Last: check.

Answer