Completing the square

Summary and Exam Tips for Completing the Square

Completing the square is a subtopic of Equations, Formulae, and Identities, which falls under the subject Mathematics in the Edexcel IGCSE curriculum. This method is used to solve quadratic equations by transforming them into the form $p(x+q)^2 + r = 0$, where $p$, $q$, and $r$ are integers. The technique simplifies the quadratic expression so that the variable $x$ appears only once, making it easier to solve.

For example, to express $2x^2 + 4x - 14 = 0$ in the completed square form, you first divide the equation by the coefficient of $x^2$, resulting in $x^2 + 2x - 7 = 0$. Then, balance the equation by adding and subtracting the square of half the coefficient of $x$, leading to $(x+1)^2 - 8 = 0$. Here, $p = 1$, $q = 1$, and $r = -8$. Practice problems, such as completing the square for $x^2 - 8x + 11$ and solving equations like $7x^2 = 4(1 + x)$, help reinforce this concept. Answers should be given in surd form for precision unless specified otherwise.

Exam Tips

• Understand the Basics: Ensure you grasp the fundamental concept of transforming a quadratic equation into the form $p(x+q)^2 + r = 0$.
• Practice Makes Perfect: Regularly solve practice questions to become familiar with the steps involved in completing the square.
• Check Your Work: Always verify your solutions by substituting back into the original equation to ensure accuracy.
• Use Surd Form: When solving, express your answers in surd form for exactness unless instructed otherwise.
• Stay Calm and Methodical: During exams, approach each problem step-by-step to avoid mistakes and manage time effectively.