# Completing the Square More Examples

5 min readBut now that we’ve turned the left side of our equation into a perfect square, all we have to do is factor like normal. There are also times when the form ax2 + bx + c may be part of a larger question and rearranging it as a(x+d)2 + e makes the solution easier, because x only appears once. Eliminate the constant [latex] – 36[/latex] on the left side by adding [latex]36[/latex] to both sides of the quadratic equation. It’s pretty much a guarantee that you’ll see quadratic equations on the SAT and ACT. But they can be tricky to tackle, especially since there are multiple methods you can use to solve them. Subtract [latex]2[/latex] from both sides of the quadratic equation to eliminate the constant on the left side.

## Applications of Completing the Square Method

Let’s quickly review the completing the square formula method steps below and then take a look at a few more examples. Express the trinomial on the left side as a perfect square binomial. Then solve the equation by first taking the square roots of both sides. Don’t forget to attach the plus or minus symbol to the square root of the constant term on the right side. We’ve already done a lot of work, and there’s still a little more to go. Now it’s time for us to solve the quadratic equation by figuring out what x could be.

As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams. This is what is left after taking the square root of both sides. Completing the square will allows leave you with two of the same factors. Remember the alternate way to write a quadratic from Figure 1 earlier on? Let’s look at it again with our current equation directly below it for reference.

## Example 1: Solve x2 + 4x + 1 = 0

Express the trinomial on the left side as a square of binomial. Solving a quadratic equation by taking the square root involves taking the square root of each side of the equation. Because this equation contains a non-squared $\bi x$ (in $\bo6\bi x$), that technique won’t work. The approach to this problem is slightly different because the value of “[latex]a[/latex]” does not equal to [latex]1[/latex], [latex]a \ne 1[/latex].

## Step 3: Apply the Completing the Square Formula to Find the Constant

Well, one reason is given above, where the new form not only shows us the vertex, but makes it easier to solve. The result of (x+b/2)2 has x only once, which is easier to use. As you can see x2 + bx can be rearranged nearly into a square … If you’d like to learn more about math, check out our in-depth interview with David Jia. Fill in the number that makes the polynomial a perfect-square quadratic. Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature.

Move the constant to the right side of the equation, while keeping the [latex]x[/latex]-terms on the left. I can do that by subtracting both sides by [latex]14[/latex]. Working with quadratic equations is just one element of algebra you’ll need to master before taking the SAT and ACT. A good place to start is mastering systems of equations, which will help you brush up on your fundamental algebra skills, too. Take top 10 most profitable crypto coins to mine in 2020 the square roots of both sides of the equation to eliminate the power of [latex]2[/latex] of the parenthesis. Make sure that you attach the plus or minus symbol to the constant term (right side of the equation).

It gives us a way to find the last term of a perfect square trinomial. We can use the perfect square identity to simplify polynomials even if they are of higher-degree than quadratics. One of the most helpful math study tools is a chart of useful mathematical equations. Luckily for you, we have a master list of the 31 formulas you must know to conquer the ACT.

- Express the trinomial on the left side as a perfect square binomial.
- But now that we’ve turned the left side of our equation into a perfect square, all we have to do is factor like normal.
- Notice that, on the left side of the equation, you have a trinomial that is easy to factor.
- This is what is left after taking the square root of both sides.

The first step is to factor out the coefficient [latex]2[/latex] between the terms with [latex]x[/latex]-variables only. If you haven’t heard of these conic sections yet,don’t worry about it. But, trust us, completing the square can come in very handy and can make your life much easier when you have to deal with certain types of equations.

Notice that you can simplify the right side of the equal sign by adding 16 and 9 to get 25. You can simplify the right side of the equal sign by adding 16 and 9. This Complete Guide to the Completing the Square includes several examples, a step-by-step tutorial, an animated video mini-lesson, and a free worksheet and answer key. Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation.

Completing the square is a helpful technique that allows you to rearrange a quadratic equation into a neat form that makes it easier to visualize or even solve. It’s used to determine the vertex of a parabola and to find the roots of a quadratic equation. If you’re just starting out with completing the square, or if the math isn’t exactly adding up, follow along with these easy steps to become a quadratic whiz. Completing the square is a technique for manipulating a quadratic into a perfect square plus a constant. The most common use of completing the square is solving quadratic equations.

We can complete the square to solve a Quadratic Equation (find where it is equal to zero). Notice that, on the left side of the equation, you have a trinomial that is easy to factor. You can always check your work by seeing by foiling the answer to step 2 and seeing if you get the correct result. Anthony is the content crafter and head educator for YouTube’s MashUp Math. You can often find me happily developing animated math lessons to share on my YouTube channel .

## Completing The Square

If you’re a visual learner, you might find it easier to watch someone solve quadratic equations instead. Khan Academy has an excellent video series on solving quadratic equations, including one video dedicated to showing you how to complete the square. YouTube also has some great resources, including this video on completing the square and this video that shows you how to tackle more advanced quadratic equations. In my opinion, the “most important” usage of completing the square method is when we solve quadratic equations. In fact, the Quadratic Formula that we utilize to solve quadratic equations is derived using the technique of completing the square. Both the quadratic formula and completing the square will let you solve any quadratic equation.