# How do you solve #2x^2-12x=-14# by completing the square?

##### 2 Answers

#### Explanation:

Write as

What process we are about to do introduces a value that is not in the original equation. So we mathematically compensate for this by the inclusion of a correction value. This correction value would turn the introduced error into 0 if we were to carry out the addition.

Suppose we had

Let

Write as

Move the power of 2 to outside the bracket

divide the 6 from

Discard the

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The error comes from the

So the error is

This has to be turned into 0 by

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Write as:

Square root both sides

#### 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

This gives:

NOW the correct value of

This gives 2 possible answers for