 # Completing the Square & Quadratic Formula

Related Topics:
Algebra Word Problems
Common Core (Algebra)
Common Core for Mathematics

Example, solutions, videos, and lessons to help High School students learn how to use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 = q that has the same solutions. Derive the quadratic formula from this form.

### Suggested Learning Targets

• Transform a quadratic equation written in standard form to an equation in vertex form (x - p)2 = q by completing the square.
• Derive the quadratic formula by completing the square on the standard form of a quadratic equation.
• Complete the square.
• Solve quadratic equations, including complex solutions, using completing the square, quadratic formula, factoring, and by taking the square root.
• Derive the quadratic formula from completing the square.
• Recognize when one method is more efficient than the other.
• Interpret the discriminant.
• Understand the zero product property and use it to solve a factorable quadratic equation
Common Core: HSA-REI.B.4a

Completing the Square 1
Part 1 of Showing how to the complete the square to solve quadratic equations.

Completing the Square 2
Part 2 of Showing how to the complete the square to solve quadratic equations. Completing the Square 3
Part 3 of Showing how to the complete the square to solve quadratic equations. Completing the Square 4
Part 4 of Showing how to the complete the square to solve quadratic equations. Completing the Square 5
Part 5 of Showing how to the complete the square to solve quadratic equations.

This video shows the proof of the quadratic formula by solving ax2+bx+c by completing the square.

Completing the Square & Quadratic Formula 1
Part 1 of completing the square. This video shows how to derive the quadratic formula by completing the square, and has a song to remember the quadratic formula. Completing the Square & Quadratic Formula 2
One more example of completing the square to solve a quadratic equation, when the coefficient of x-squared is not 1. The problem is also solved using the quadratic formula.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 