Some quadratic equations are difficult to solve, and some quadratic equations are easy to solve. Depending on how the equation is provided, certain methods can be very straightforward. Consider the equation 5 = (x + 3)^{2}. We can find solutions to x by performing inverse operations, just like we solve other multistep equations:

Our equation  

Take square root of both sides  

Subtract 3 from both sides  

Our exact solutions  

Our approximate solutions 
Unfortunately, not all quadratic equations come in this form. However, we can manipulate the equation to write it as such. This requires a process known as completing the square.
To understand the mechanics of completing the square, it is helpful to connect it to the FOIL process. Let's take the general expression (x + a)^{2} and FOIL it:




Two factors of  

FOIL  

Combine like terms 
The process of completing the square follows a specific set of steps in order to convert the equation into one similar to our very first example:
Let's apply these steps to the equation:

Our quadratic formula  

Add 14 to both sides  

Divide equation by 2  

Divide by 2, then square it 


Add 9 to both sides  

Simplify the left side  

Write right side as binomial squared 
Now that we have converted an equation from standard form into a binomial squared, we can solve this equation following the same procedure as our very first example:

Our quadratic formula  

Take square root of both sides  

Simplify the left side  

Add 3 to both sides  

Create two equations due to  

Our solutions 