Question

What is the intermediate step in the form (x + a)^2 = b as a result in completing the square for the following equation?

Answer 1

For this case we have the following expression:

We follow the steps below:

We subtract 4x on both sides of the equation:

We subtract 10 from both sides of the equation:

Now, we must complete squares.

When we have an equation of the form:

, if we want to complete squares we must subtract c on both sides of the equation obtaining:

The square is completed by adding to both sides of the equation:  

So, we have left:

In the given expression we have:

And to complete the square we have:

Rewriting we have:

We factor the left side of the equation, that is, we look for two numbers that when added together result in -8 and when multiplied as a result 16. We have:

So, we have:

Answer:

The intermediate step is to complete squares