Choose a method: 2x^2 + 3x - 4 = 0

Step by step

The question

Question: choose a method and solve 2x² + 3x − 4 = 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 = −8 and add to b = 3.

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 = 2 is with x², b = 3 is with x, c = −4 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.

3 squared is 9.

4 times 2 times −4 is −32.

9 take away −32 is 41.

So under the root we have 41.

41 is not a square number.

We keep √41.

So x = (−3 + √41)/4 or x = (−3 − √41)/4.

With a calculator: x is about 0.85 or about −2.35.

Let's look back.

First: choose the method.

Then: find a, b and c.

Last: use the formula.