Step by step
The question
Question: choose a method and solve (x + 2)² = 5.
(x + 2)2 = 5
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 5.
So that something is the square root of 5, or minus it.
Both work, because minus times minus is plus.
( )² = k → ( ) = √k or −√k
5 is not a square number, so we keep √5.
x + 2 = √5 or x + 2 = −√5
3 Get x alone
To remove the + 2, we take away 2 on both sides.
We do it in both equations.
x = √5 − 2 or x = −√5 − 2
So x = √5 − 2 or x = −√5 − 2.
With a calculator, √5 is about 2.24.
So x is about 0.24 or about −4.24.
x ≈ 0.24 or x ≈ −4.24
Let's look back.
First: choose the method.
Then: square root of both sides.
Last: get x alone.
Answer
x ≈ 0.24 or x ≈ −4.24