How do you use the completing the square method to solve a quadratic equation?

First you need to get the quadratic equation in completed square form. 
This looks like: (x+p)^2 + q 

To put an expression in completed square form you can use this formula: x^2 + 2bx + c = (x+b)^2 - b^2 + c

Once in this form you can solve the equation for x by rearranging. 

For example: solve x^2 + 4x -5=0 using the completing the square method.

Using the formula with b = 2 and c = -5 gives: (x+2)^2 – 2^2 – 5 = 0

And simplifying leads to:

(x+2)^2 – 9 = 0 Rearranging gives:

(x+2)^2 = 9

x + 2 = ± 3

x = - 2 ± 3 

So the answers are:

x = 1 or x= -5

Answered by Caroline P. Maths tutor

3066 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

A line joins 2 points (2,9) and (5,4). Calculate the gradient of the straight line and then write down the equation of the straight line.


3x² = 75 Find the value of x.


There is a right angled triangle, you know the length of the hypotenuse (6) and one other side (3), can you calculate the third side of the triangle?


How do you expand (2x+9)^2?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences