Year 10 - Maths
Solving complex quadratic equations by completing the square
Algebraic manipulation
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In algebraic manipulation, pupils use apply knowledge of the distributive law to find the product of two binomaials in order to factorise quadratics.
Lesson Summary
You will learn to solve more complex quadratic equations algebraically by completing the square.
Key Notes
- There are other methods to find the solutions of a quadratic equation.
- One of these methods is called completing the square.
- Completing the square is useful when the quadratic cannot be easily factorised.
- Quadratic equations of the form $$ax^2 + bx + c = 0$$ (where $$a$$ ≠ 1) can be solved by completing the square.
Vocabulary To Learn
- Completing the square: Completing the square is the process of rearranging an expression of the form ax^2 + bx + c into an equivalent expression of the form a(x + p)^2 + q
Common Mistakes To Avoid
- Pupils may believe that to write in completed square form they can divide through by the coefficient of x^2
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There are other methods to find the solutions of a quadratic equation. One of these methods is called completing the square.
2. Use this key word in a maths sentence and explain it clearly. 'Completing the square'
Completing the square is the process of rearranging an expression of the form ax^2 + bx + c into an equivalent expression of the form a(x + p)^2 + q. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may believe that to write in completed square form they can divide through by the coefficient of x^2. Correction: This works for equations as equality can be maintained by dividing both sides of the equation. However if manipulating an expression, dividing through by a value changes the expression. Instead a value can be 'factored out' as necessary.
More Lessons In This Unit
- Advanced problem solving with algebraic manipulation Study Guide
- Checking and securing understanding of changing the subject Study Guide
- Checking and securing understanding of expanding a single bracket Study Guide
- Checking and securing understanding of factorising Study Guide
- Checking and securing understanding of forming linear equations Study Guide
- Checking and securing understanding of simplifying Study Guide
- Checking and securing understanding of solving and interpreting linear equations Study Guide
- Checking and securing understanding of substitution Study Guide
- Checking and securing understanding of the product of two binomials Study Guide
- Factorising a quadratic expression Study Guide
- Factorising quadratics of the form ax^2 + bx + c Study Guide
- Factorising using the difference of two squares Study Guide
- Further algebraic terminology Study Guide
- Problem solving with algebraic manipulation Study Guide
- Solving quadratic equations by completing the square Study Guide
- Solving quadratic equations by factorising Study Guide
- Solving quadratic equations by factorising where rearrangement is required Study Guide
- Solving quadratic equations by using the formula Study Guide
- The product of three binomials Study Guide
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