# How do you solve using the completing the square method #x^2 – 8x = –11#?

##### 1 Answer

My answer was meant to help rapidly. Stress can make students unable to process explanations. Now on to the explanation.

If you have an equation of the type

you know how to solve.

What if you have terms linear in x too? Well this is your lucky day.

For you know that

If you stare at this equation long enough, you see that the right hand side has a term in x, but the left hand side is a square. No x. And if it's a square, you know how to solve, right?

So all you need is to work BACKWARD. From the right hand side to the left hand side.

Let's do it.

The linear term in our equation is

This gives you

So that

So your original equation now reads

move 16 to the other side

This is an equation of the second degree. It has two roots, since 5 is positive.

These are

Back to x. Two solutions

And you're done :)