Enter the variables a, b, and c into the calculator below to calculate the two solutions to completing the square.

Completing The Square Formula

{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }

When completing the square, the above formula is used where a, b, and c are variables from the equation


Completing the Square Definition

Completing the square is a mathematical technique to rewrite a quadratic equation in a specific form. By rearranging the equation, it allows us to easily identify the vertex or turning point of the parabola represented by the equation.

To complete the square, we take a quadratic equation as “ax^2 + bx + c” and manipulate it to create a perfect square trinomial. This is done by adding or subtracting a constant term to both sides of the equation, which is calculated using a specific formula involving the coefficient of the middle term.

The resulting quadratic equation in completed square form, “a(x – h)^2 + k”, clearly reveals the coordinates (h, k) of the vertex of the parabola. The value of “h” represents the horizontal shift from the origin, while “k” indicates the vertical shift. This information is crucial as it provides insight into the shape, location, and orientation of the parabola.

Completing the square is important because it simplifies graphing quadratic equations. By converting the equation into completed square form, we can easily determine the vertex, a key point on the graph. This lets us quickly sketch the parabola and understand its behavior without plotting numerous points.

How to calculate completing the square?

How to complete the square

  1. First, determine the variables

    Calculate or gather the variables a,b, and c from an equation of the form ax^2+bx+C.

  2. Enter the variables into the formula or calculator above.

    The solution should be two separate answers, typically the x-intercepts.


What does completing the square mean?

Completing the square is another way of saying using the quadratic equation to solve for the x-intercepts of an equation in the form mentioned above.

How do i complete the square?

Follow the steps in the how-to guide above to complete the square.