Step by step
The question
Question: solve x² + 4x − 1 = 0.
x2 + 4x − 1 = 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 = 4 is with x, c = −1 is the plain number.
a = 1, b = 4, c = −1
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 = −4 ± √42 − 4 × 1 × (−1)2 × 1
4 squared is 16.
4 times 1 times −1 is −4.
16 take away −4 is 20.
4² = 16
4 × 1 × (−1) = −4
16 − (−4) = 20
So under the root we have 20.
x = −4 ± √202
√20 = √4 × √5 = 2√5
20 is not a square number.
20 is 4 times 5, and √4 is 2.
So √20 is 2√5.
x = −4 ± 2√52
Every part on top can be divided by 2.
−4 divided by 2 is −2.
2 divided by 2 is 1.
−4 ÷ 2 = −2, 2 ÷ 2 = 1
So the answer is shorter now.
x = −2 ± √5
So x = −2 + √5 or x = −2 − √5.
With a calculator: x is about 0.24 or about −4.24.
x ≈ 0.24 or x ≈ −4.24
Let's look back.
First: find a, b and c.
Last: use the formula.
Answer
x ≈ 0.24 or x ≈ −4.24