Step by step
The question
Question: solve x² + 2x + 5 = 0.
x2 + 2x + 5 = 0
1 Find a, b and c
It does not split into brackets with whole numbers, so we use the formula.
First we read the numbers: a = 1 is with x², b = 2 is with x, c = 5 is the plain number.
a = 1, b = 2, c = 5
2 Use the formula
Here is the formula.
It works for every equation like this.
x = −b ± √b2 − 4ac2a
We put the numbers in, each in brackets.
x = −2 ± √22 − 4 × 1 × 52 × 1
2 squared is 4.
4 times 1 times 5 is 20.
4 take away 20 is −16.
2² = 4
4 × 1 × 5 = 20
4 − 20 = −16
So under the root we have -16.
x = −2 ± √-162
−16 is negative.
No real number squared is negative, so there is no real solution.
x = no real solution
Let's look back.
First: find a, b and c.
Last: use the formula.
Answer
x = no real solution