Completing the Square

Completing the square

• If a quadratic expression is written in the form (x+p)^2 + q it is in completed square form
• You can solve quadratic equations which don’t have integer answers by completing the square

Useful identities

• If you learn these two identities you can save time when you are completing the square
• x^2 + 2bx + c = (x+b)^2 - b^2 + c
• x^2 - 2bx + c = (x-b)^2 -b^2 + c

Positive and negative roots

• Remember that any positive number has two square roots, one positive and one negative
• If you ‘square root’ both sides of an equation you need to use +- to show that there are two square roots