In mathematics, completing the square is a technique for transforming a quadratic equation into a form that can be more easily solved. It is a particular case of the more general process of completing the square in algebra.
The basic idea is to rewrite the equation in the form where is a number that is both a square root of and non-zero. You can do this by taking the square root of both sides of the equation and dividing both sides by to get this is the same equation as before, but now the coefficient is 1. The equation can solve by using the standard methods for solving quadratic equations.
The Quadratic Formula Calculator helps students to solve quadratics quickly and easily. With Quadratic Formula Calculator, students can determine the solutions of any quadratic equation by entering its coefficients into the calculator.
Completing the square is a mathematical technique often used to solve quadratic equations. The general form of a quadratic equation is ax^2 + bx + c = 0. To complete the square, we need to find values for a, b, and c that will make the equation take on the form (x-h)^2 + k = 0.
Different Methods
A few different methods can be use to complete the square. One method is to factor the quadratic equation into two linear factors. Another way is to use the quadratic formula. The quadratic formula can be used to solve for x in any quadratic equation.
Perfect Square Trinomial
The most common method of completing the square is to use the fact that a perfect square trinomial can be written in the form (x-h)^2 + k. We can use this fact to rewrite our quadratic equation in the form (x-h)^2 + k = 0.
The Quadratic Formula Calculator also allows students to solve perfect square trinomials (PSTs) efficiently.
To complete the square, we first need to identify the values of a, b, and c that will make the equation take on this form. Let’s start with an example equation: x^2 + 6x + 9 = 0. In this equation, a = 1, b = 6, and c = 9.
To complete the square, we need to find values for h and k that will make the equation (x-h)^2 + k = 0. We can do this by using the fact that a perfect square trinomial can be written in the form (x-h)^2 + k.
To find the value of h, we need to find the value of x that will make the equation (x-h)^2 = 0. This value is called the vertex of the parabola. The vertex is the point where the parabola changes direction. In our example equation, the vertex is at x = -3.
To find the value of k, we need to plug the value of h (x = -3) into the original equation and solve for k. In our example equation, this gives us k =
Square root
Another way to complete the square is to take the square root of both sides of the equation and then add or subtract a number from both sides.
For example, if you have the equation x^2 + 2x + 1 = 0, you can take the square root of both sides to get x^2 + 2x = -1. Then, you can add 1 to both sides to get x^2 + 2x + 1 = 0. This can be helpful because it means that you can now factor the left side of the equation as (x + 1)^2 = 0. This can be a much easier equation to work with, and it can sometimes be helpful in solving problems.
yet another way to complete the square is to take the square root of both sides of the equation and then multiply both sides by a number.
For example, if you have the equation x^2 + 2x + 1 = 0, you can take the square root of both sides to get x^2 + 2x = -1. Then, you can multiply both sides by -1 to get x^2 – 2x = 1.
Applications of completing the square
Completing the square is a method to solve certain algebraic equations, most notably quadratic equations. The name derives from the fact that the procedure can be used to “complete the square” of a trinomial.
Completing the square can also be used to find the center and radius of a circle, given an equation in standard form. The process is relatively simple once you understand the steps and principles involved.
Decreasing the time and energy spent solving quadratics equations is easy when you complete the square like a pro. Not only does this method give you the solution to even the most complex algebra problems quickly and easily, it also separates other variables to allow for simpler calculation of what might be a hidden unknown.
