Step by step
The question
Question: solve x² − 2x − 4 = 0.
x2 − 2x − 4 = 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 = −4 is the plain number.
a = 1, b = −2, c = −4
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) ± √(−2)2 − 4 × 1 × (−4)2 × 1
−2 squared is 4.
4 times 1 times −4 is −16.
4 take away −16 is 20.
(−2)² = 4
4 × 1 × (−4) = −16
4 − (−16) = 20
So under the root we have 20.
x = 2 ± √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 = 2 ± 2√52
Every part on top can be divided by 2.
2 divided by 2 is 1.
2 divided by 2 is 1.
2 ÷ 2 = 1, 2 ÷ 2 = 1
So the answer is shorter now.
x = 1 ± √5
So x = 1 + √5 or x = 1 − √5.
With a calculator: x is about 3.24 or about −1.24.
x ≈ 3.24 or x ≈ −1.24
Let's look back.
First: find a, b and c.
Last: use the formula.
Answer
x ≈ 3.24 or x ≈ −1.24