Completing the Square to Solve Quadratic Equations

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Examples, solutions and videos to help GCSE Maths students learn how to complete the square in order to solve quadratic equations.

The following diagram gives the steps for the completing the square method for solving quadratic equations. Scroll down the page for more examples on using the completing the square method.
Completing the Square

How to solve quadratic equations by completing the square?

  1. If a ≠ 1, divide each term of the quadratic equation by a.
  2. Write the quadratic in the form
    x2 + bx + ____ = c + ____
  3. Add (b/2)2 to both sides of the equation.
  4. Factor the left side of the equation. It should be a perfect square.
  5. Square root both sides of the equation and solve for x.

GCSE Maths - Quadratic Equations 6 (Completing the Square) Higher Mathematics (IGCSE)

Quadratic Equation Completing the Square GCSE Maths revision Exam paper practice & help

Completing the square for a quadratic equation where the coefficient of x2 is greater than 1
This tutorial runs through completing the square for a quadratic expression where the coefficient of x squared is greater than 1.
Completing the Square when the Leading Coefficient is not 1

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.
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