Step by step
The question
Question: solve x² + 1 > 0.
There is an x², so the answer can be two parts.
x2 + 1 > 0
1 Does it cross 0?
It does not factor.
Let's look at b² − 4ac, the part under the root in the formula.
It is −4, negative.
b² − 4ac = 0 − 4 = −4
Negative under the root: no x makes it 0.
So it never crosses 0: it is always plus, or always minus.
x2 + 1 : never 0
Test one number, x = 0: it gives 1.
Plus.
So it is always plus.
x = 0: 1 +
2 Read the answer
It is always plus, so it is always greater than 0.
Every number works.
= every number works
Let's look back.
First: does it cross 0?.
Last: read the answer.
Answer
= every number works