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. is positive because any number squared is positive. This is because if b is negative, then the constant in the binomial will need to be negative as well. Notice that there are cases where you will subtract. Solve the following quadratic equation by completing the square method. 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. The calculator solution will show work to solve a quadratic equation by completing the square to solve the entered equation for real and complex roots. A perfect square trinomial is a trinomial that will factor into the square of a binomial. This calculator is a quadratic equation solver that will solve a second-order polynomial equation in the form ax 2 + bx + c 0 for x, where a 0, using the completing the square method. 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.

Completing the square video tutorial