Choose a method: x^2 - 6x + 2 = 0

Step by step

The question

Question: choose a method and solve x² − 6x + 2 = 0.

1 Choose the method

We ask in order.

First: is there no x term?

No, there is one.

Does it factor easily?

No two whole numbers work.

Neither of these.

The formula works for every quadratic equation.

So we use it.

So: the formula.

2 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 = −6 is with x, c = 2 is the plain number.

3 Use the formula

Here is the formula.

It works for every equation like this.

We put the numbers in, each in brackets.

−6 squared is 36.

4 times 1 times 2 is 8.

36 take away 8 is 28.

So under the root we have 28.

28 is not a square number.

28 is 4 times 7, and √4 is 2.

So √28 is 2√7.

Every part on top can be divided by 2.

6 divided by 2 is 3.

2 divided by 2 is 1.

So the answer is shorter now.

So x = 3 + √7 or x = 3 − √7.

With a calculator: x is about 5.65 or about 0.35.

Let's look back.

First: choose the method.

Then: find a, b and c.

Last: use the formula.