Choose a method: 5x^2 + 2x - 1 = 0

Step by step

The question

Question: choose a method and solve 5x² + 2x − 1 = 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 multiply to a × c = −5 and add to b = 2.

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.

The formula works for every equation like this, so we use it.

First we read the numbers: a = 5 is with x², b = 2 is with x, c = −1 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.

2 squared is 4.

4 times 5 times −1 is −20.

4 take away −20 is 24.

So under the root we have 24.

24 is not a square number.

24 is 4 times 6, and √4 is 2.

So √24 is 2√6.

So x = (−2 + 2√6)/10 or x = (−2 − 2√6)/10.

With a calculator: x is about 0.29 or about −0.69.

Let's look back.

First: choose the method.

Then: find a, b and c.

Last: use the formula.