How many solutions x^2 + 8x + 16 = 0 Step by Step

Step by step

The question

Question: find the number of real solutions of x² + 8x + 16 = 0.

x² + 8x + 16 = 0

1 Find a, b and c

We read the numbers: a = 1 is with x², b = 8 is with x, c = 16 is the plain number.

a = 1, b = 8, c = 16

2 Work out b² − 4ac

In the formula, b² − 4ac is under the square root.

It is called the discriminant.

Its sign tells us how many solutions there are.

x = −b ± √b² − 4ac2a

We put the numbers in, each negative one in brackets.

b² − 4ac = 8² − 4 × 1 × 16

8² is 64.

4 times 1 times 16 is 64.

8² = 8 × 8 = 64

4 × 1 × 16 = 64

Careful!

b is squared first: b² means 8 times 8, not 8.

Careful: not 8 − 64 ✗

So we have 64 take away 64.

= 64 − 64

So the discriminant is 0.

= 0

3 How many solutions

It is 0.

The square root of 0 is 0.

Plus 0 and minus 0 give the same answer.

So there is just one.

positive → 2 real solutions

0 → 1 real solution

negative → no real solutions

So x² + 8x + 16 = 0 has 1 real solution.

= 1 real solution

4 Check

Let's check with the formula.

Under the root we get 0, and the square root of 0 is 0.

x = −8 ± √02 = −8 ± 02

Plus 0 and minus 0 give the same number: x = −4.

One solution.

It works!

x = −4 only

Let's look back.

First: find a, b and c.

Then: work out b² − 4ac.

Then: how many solutions.

Last: check.

Answer