# How do you solve #x^2 + 8x + 2 = 0# by completing the square?

##### 2 Answers

#### Explanation:

We will use the difference of squares identity, which can be written:

#a^2-b^2 = (a-b)(a+b)#

with

#0 = x^2+8x+2#

#=(x+4)^2-16+2#

#=(x+4)^2-(sqrt(14))^2#

#=((x+4)-sqrt(14))((x+4)+sqrt(14))#

#=(x+4-sqrt(14))((x+4+sqrt(14))#

Hence:

#x = -4+-sqrt(14)#

#### Explanation:

Completing the square is based on the consistency of the answers to the square of a binomial.

In all of the products above,

The first and last terms,

There is a specific relationship between 'b' - the coefficient of the

Knowing this, it is always possible to add in a missing value for

In

It is therefore moved to the right hand side and the wanted value of

This gives 2 possible answers for