Step by step
The question
Question: solve (x + 1)² = 7.
(x + 1)2 = 7
1 Square root of both sides
Something squared is 7.
So that something is the square root of 7, or minus it.
Both work, because minus times minus is plus.
( )² = k → ( ) = √k or −√k
7 is not a square number, so we keep √7.
x + 1 = √7 or x + 1 = −√7
2 Get x alone
To remove the + 1, we take away 1 on both sides.
We do it in both equations.
x = √7 − 1 or x = −√7 − 1
So x = √7 − 1 or x = −√7 − 1.
With a calculator, √7 is about 2.65.
So x is about 1.65 or about −3.65.
x ≈ 1.65 or x ≈ −3.65
Let's look back.
First: square root of both sides.
Last: get x alone.
Answer
x ≈ 1.65 or x ≈ −3.65