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# Completing the Square in Math

## Examples & Formula for completing the square

Objective The goal of this web page is to explain how to complete the square, how the formula works and provide lots of practice problems.
On a different page, we have a completing the square calculator which does all the work for this topic. You just enter the quadratic.

## So, what does it really do for us?

Formula for Completing the Square
To best understand the formula and logic behind completing the square, look at each example below and you should see the pattern that occurs whenever you square a binomial to produce a perfect square trinomial.

Practice Problems

Directions Find the missing value to complete the square

Problem 1) $$x^2 + \color{red}{16}x + \blacksquare$$
 Step 1

Problem 2) $$x^2 + \color{red}{20}x + \blacksquare$$
 Step 1

Problem 3) $$x^2 + \color{red}{18}x + \blacksquare$$
 Step 1

Problem 4) $$x^2 + \color{red}{5}x + \blacksquare$$
 Step 1

Problem 5) $$x^2 + \color{red}{7}x + \blacksquare$$
 Step 1
II. Completing Square when a is not 1

## What about $$\color{blue}{3}x^2 + 18x$$, what then ?

Practice Problems

Problem 6) $$2x^2 + 12x + \blacksquare$$
 Step 1

Problem 7) $$3x^2 + 36x + \blacksquare$$
 Step 1

Problem 8) $$5x^2 + 20x + \blacksquare$$
 Step 1

The next problems are quite challenging, good luck!

Problem 9) $$2ax^2 + 12ax + \blacksquare$$
 Step 1

Problem 10) $$3x^3 + 18x^2 + \blacksquare$$
 Step 1

Problem 11) $$4x^3 + 2x^2 + \blacksquare$$
 Step 1