What is completing the square and how do I do it?

Completing the square is a method of solving quadratic equations that can't be factorised. The end goal is to express the quadratic in the form:(x + a)2 = -bWhich allows us to root both sides and find our solutions for x.Let's do an example. We'll complete the square for the quadratic:x2 + 8x + 4 = 0First, we group the x terms together in a bracket to make the process a little easier to visualise:(x2 + 8x) + 4 = 0We're then going to rewrite (x2 + 8x) as (x + 4)2 - 42. We've done this by moving the square to the outside of the bracket, removing the x from the second term, halving the second term's coefficient, and squaring this number and then taking it away from the outside of the bracket. We can see that these are equal expressions by expanding them out:x2 + 8x = (x + 4)(x + 4) - 42 = x2 + 8x + 16 -16x2 + 8x = x2 + 8xPutting this back into the equation we started with, we get:(x + 4)2 + 4 - 16 = 0(x + 4)2 - 12 = 0(x + 4)2 = 12In order to find our solutions for x, we now root both sides, remembering that the root of a positive number gives us two answers: one negative and one positive:x + 4 = ±√(12)So, x = -4 ±√(12)

HJ
Answered by Henry J. Maths tutor

3292 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

I buy a car from a dealership for £3500. The car depreciates in value for every year I own it. What is the value of the car after I have owned it for 18 months if it depreciates at a rate of 5 percent?


Solve the simultaneous equations: 3x+y=11 and 2x+y=8.


Increase 32 million by 4%. Give your answer correct to the nearest million.


Divide 711 in the ratio 4:5


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