Complete the Square (Solve Quadratic)

Examples, videos and lessons to help High School students learn to choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A. Factor a quadratic expression to reveal the zeros of the function it defines.

B. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Suggested Learning Targets

Write quadratics expressions in equivalent forms by completing the square.

Completing the Square Example - Solve Quadratic Equations
Example:
2x² - 6x + 3 = 0

Completing the square.
Example:
3x² - 18x - 15 = 0

• Show Step-by-step Solutions

Solving Quadratic Equations by Completing the Square.
Examples:
x² - 6x = 5
10x² - 30x - 4 = 0

Completing the Square to Solve Quadratic Equations.
Example:
3x² - 1 = 12x

• Show Step-by-step Solutions

Completing the Square to Solve Quadratic Equations.
Example:
-5x² + 3x = -2

• Show Step-by-step Solutions

Completing the Square - Solving Quadratic Equations
Example:
x² - 6x + 8

• Show Step-by-step Solutions

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

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.