Choose a method: x^2 + 2x + 7 = 0 Step by Step

Step by step

The question

Question: choose a method and solve x² + 2x + 7 = 0.

x² + 2x + 7 = 0

1 Choose the method

We ask in order.

First: is there no x term?

No, there is one.

1. no x term, or ( )² = k? ✗

Does it factor easily?

No two whole numbers work.

2. factors easily? ✗

Neither of these.

The formula works for every quadratic equation.

So we use it.

So: the formula.

3. anything else ✓ 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 = 2 is with x, c = 7 is the plain number.

a = 1, b = 2, c = 7

3 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 ± √2² − 4 × 1 × 72 × 1

2 squared is 4.

4 times 1 times 7 is 28.

4 take away 28 is −24.

2² = 4

4 × 1 × 7 = 28

4 − 28 = −24

So under the root we have -24.

x = −2 ± √-242

−24 is negative.

No real number squared is negative, so there is no real solution.

x = no real solution

Let's look back.

First: choose the method.

Then: find a, b and c.

Last: use the formula.

Answer