Solving Quadratic Equations – Completing the Square It is assumed you have already watched the slideshow demonstrating how to complete the square on a binomial. Completing the Square is a method that can be used to solve any quadratic equation The previous methods of factoring and square roots to solve quadratics were limited, in that there are many quadratic equations that neither method would solve.

Solving a Quadratic Equation by Completing the Square 1.Write the equation in the form 2.Complete the square 3.Factor the perfect square trinomial 4.Solve using the square root method

Example 1: Note that the equation is already in the proper form. Complete the square. Solve the equation. Add this value to both sides of the equation.

Complete the problem using the square root method. Factor

Example 2: Write the equation in the proper form. Complete the square. Be sure to add the same value to both sides of the equation. Solve the equation.

Complete the problem using the square root method. Factor

Example 3: Write the equation in the proper form. Complete the square and add to both sides. Solve the equation. Simplify

Complete the problem using the square root method. Factor

Use the common denominator to combine the fractions.

Example 4: Write the equation in the proper form. Divide by 3 which is the coefficient of the quadratic term. Solve the equation. To be able to complete the square, the coefficient of the quadratic term must be 1.

Complete the square. Factor Complete the problem using the square root method.

Example 5: Write the equation in the proper form. Complete the square. Solve the equation. Factor

Complete the problem using the square root method.