Tutorial

GCSE Maths: Solving Quadratics by Completing the Square

Learn how to solve a quadratic equation using the completed square form.
A sunlit, freshly tilled garden plot seen from a low angle, with a single, perfectly formed square section highlighted by brighter sunlight, ready for planting.

Management & Tools

Deck Contents

18 Cards
Lesson#1
In the previous deck, we learned how to rewrite a quadratic expression by completing the square. Now, we'll use that skill to solve quadratic equations. This means finding the specific values of x that make the equation true.
Lesson#2
Let's start with an equation we want to solve, for example, x squared plus 6x plus 5 equals 0. After completing the square, this equation can be rewritten as: open bracket x plus 3 close bracket squared, minus 4, equals 0.
Quiz#3
When solving a quadratic equation that is in completed square form, what is the first main goal?

Isolate the squared bracket

Lesson#4
To isolate the squared bracket in our example, which is 'open bracket x plus 3 close bracket squared, minus 4, equals 0', we need to get rid of the minus 4. We do this by adding 4 to both sides of the equation. This leaves us with 'open bracket x plus 3 close bracket squared equals 4'.
Quiz#5
To solve the equation 'open bracket x plus 5 close bracket squared, minus 9, equals 0', what is the first algebraic step?

Add 9 to both sides

Lesson#6
Now that we've isolated the squared part, our equation is 'open bracket x plus 3 close bracket squared equals 4'. The next step is to undo the square. The opposite, or inverse, of squaring something is to take its square root.

Login to View Content

Create a free account or log in to see all 18 cards and start studying this deck.

Learn GCSE Maths: Solving Quadratics by Completing the Square differently

Auracle is an audio-first learning platform built for busy people. Memorize anything without looking at a screen.

Hands-Free Learning

Listen, interact, and review cards entirely through audio. Perfect for commuting, walking, or at the gym.

Spaced Repetition

Auracle uses a scientific algorithm to schedule your reviews at the optimal time, ensuring you never forget what you learn.

Learn how it works

Ready to start the GCSE Maths: Solving Quadratics by Completing the Square audio deck?