If you’re like most people, you probably learned how to completing the square easy in algebra class. But what exactly is it? And why is it important? In mathematics, “completing the square” is a technique used to solve certain quadratic equations.
It’s also a handy tool to have in your algebra toolbox because it can be used to simplify equations, make them easier to solve, and sometimes even help you find the roots of an equation. In this blog post, we’ll take a closer look at what completing the square is and how it can be used. We’ll also give you some tips on how to do it so you can add this valuable skill to your algebra repertoire.
What is completing the square?
Completing the square is a mathematical technique used to solve certain quadratic equations. The general form of a quadratic equation is ax^2 + bx + c = 0. To complete the square, one must first determine the value of b/2a. This value is then squared and added to both sides of the equation. The result is a new equation in the form (x-b/2a)^2 = -c/a + (b/2a)^2. This process can be used to solve for x, or to find the vertex of a parabola when graphed.
The different types of quadratic equations
Quadratic equations come in many different forms, but can generally be classified into one of three types: standard form, factored form, or vertex form. Standard form is the most commonly used form, and is typically what is taught in algebra classes. It looks like this: ax^2 + bx + c = 0. Factored form is less common, but can be very useful when trying to solve certain types of quadratic equations.
It takes the standard form equation and factors it into two linear terms multiplied together: (ax + b)(cx + d) = 0. Vertex form is the least common type of quadratic equation, but can be helpful in graphing quadratics. It takes the standard form equation and rearranges it so that all of the terms are squared: a(x-h)^2 + k.
How to complete the square
In order to complete the square, you will need to take the following steps:
1) Determine what is needed in order to complete the square. This will usually involve finding the value of a certain term in the equation that will make it easier to solve.
2) Manipulate the equation so that all terms are on one side of the equal sign, with zero on the other side.
3) Use the quadratic formula to solve for the unknown variable.
4) Substitute your answer back into the original equation to check your work.
Completing the square with negative numbers
Negative numbers can be a little trickier to work with when completing the square, but it is still possible. To start, let’s look at the equation:
x^2 – 6x + 9 = 0
To complete the square, we need to find a number that we can add to both sides of the equation so that the left side is a perfect square. In this case, we can add -9 to both sides:
x^2 – 6x + 9 – 9 = 0 – 9
Now we have:
x^2 – 6x = -9
We can now finish by adding 9 to both sides again:
x^2 – 6x + 9 = -9 + 9
And we are left with: x^2-6x+9=0
Why is completing the square important?
There are a few reasons why completing the square is important. For one, it allows you to solve equations that would otherwise be impossible to solve. It also makes solving certain types of equations much easier. Finally, it can give you a better understanding of the underlying concepts in algebra.
Conclusion
Completing the square is a handy mathematical technique that can be used to solve quadratic equations. In this article, we have looked at how to complete the square for both positive and negative values of x. We have also seen how completing the square can be used to find the vertex of a parabola. I hope that you have found this article to be helpful and that you now feel confident in your ability to complete the square.
