# How do you solve the quadratic #3x^2-2x=2x+7# using any method?

##### 2 Answers

#### Answer:

#### Explanation:

Given:

Subtract

7 is a prime number so does not share any common factors other than 1 with the other coefficients.

Compare to the standardised equations:

Where

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#### Answer:

Same solution but using completing the square. The process introduces an error that has to be corrected by the inclusion of

Takes longer to explain than do the maths.

#### Explanation:

Given:

Write as:

Let the constant of correction be

At this point

Write as:

Take the square from

Halve the coefficient of

Now get rid of the

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We now have to find the value of

The error comes from the term

Equation(1)

Equation(2)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So from equation(2) we have

So equation(2) becomes:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~