The objective of completing the square is to satisfy the above two conditions. The trinomial does not contain the coefficient a, or rather, a = 1 If we go back to the standard form of the quadratic equation, ax 2 + bx + c = 0, you will notice two differences between this perfect square trinomial and the quadratic:ġ. These include the solution of quadratic equations. To complete the square on this equation, we must first isolate the terms involving x as. Completing the square is an algebraic technique which has several applications. a typical quadratic equation in standard form. is positive because any number squared is positive. We will illustrate each of the steps in completing the square using the following example, y 2x 2 - 8x + 10.
Completing the square video tutorial plus#
This is because if b is negative, then the constant in the binomial will need to be negative as well. After reading this text, and/or viewing the video tutorial on this topic, you should be able to: write a quadratic expression as a complete square, plus or minus a constant solve a quadratic equation by completing the square Contents 1. Notice that there are cases where you will subtract. If we square this binomial, the perfect square trinomial needed to complete the square will equal: Therefore, the binomial used to complete the square is: As you can see, the coefficient of x is 2n.įor a quadratic of the form x 2 + bx + c, the coefficent of x is already b, so we only need to figure out the value of the constant c.
The square of a binomial is a binomial multiplied by itself.īinomials of the form x + n, where n is some constant, are some of the easier binomials to work with. A perfect square trinomial is a trinomial that will factor into the square of a binomial. Generally, the goal behind completing the square is to create a perfect square trinomial from a quadratic. It can also be used to convert the general form of a quadratic, ax 2 + bx + c to the vertex form a(x - h) 2 + k Home / algebra / solving equations / completing the square Completing the squareĬompleting the square is a method used to solve quadratic equations.
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