Find the roots of the quadratic equation, x^2 - 8x + 24 = 0, by completing the square.

Step 1:

The fisrt step is to use the following formula when asked to complete the square,

( x + (b/2) )2 - (b/2)2 + c = 0

Step 2

In our case, b=8,c=24

Hence our equation,

x2 - 8x + 24= 0


(x + (-8/2) )2 - (-8/2)2 + 24 = 0

which is equal to

(x - 4 )2 - (4)2 + 24 = 0

(x - 4 )2 - 16 + 24 = 0

(x - 4 )2 + 8 = 0

Step 3:

Now we take 8 to the RHS, as this will allow us to take the square root of both sides.

(x - 4 )2 = -8

(x - 4 ) = +/- (-8)1/2

x = 4 +/- (-8)1/2

Hence the roots of x2 - 8x + 24= 0 are

x = 4 + (-8)1/2  and x = 4 - (-8)1/2

Pantelis K. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor

7 months ago

Answered by Pantelis, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£18 /hr

Andrew B.

Degree: Economics L100 (Bachelors) - Exeter University

Subjects offered: Maths, Economics


“About Me: I am an economics student at Exeter University, I have a real passion for economics and how applicable it is to the world around us, and I hope my enthusiasm for it comes across in my tutorials and helps to inspire you! I'm...”

£18 /hr

Emily L.

Degree: Law (Bachelors) - Durham University

Subjects offered: Maths, English Literature+ 1 more

English Literature

“I am a first year undergraduate reading Law at Durham University. Prior to this, I attended the Tiffin Girls' School in Kingston upon Thames where I studied English Literature, Chemistry and Fine Art at A2 Level (with additional Mathe...”

£18 /hr

Jamie P.

Degree: Architecture (K100) (Bachelors) - Sheffield University

Subjects offered: Maths, Geography+ 1 more

Further Mathematics

“Hello! I am an Architecture student at The University of Sheffield. I would like to say I am creative, friendly and approachable, and willing to work hard in all aspects of what I do. My personable and easy-going nature will help to b...”

MyTutor guarantee

About the author

Pantelis K.

Currently unavailable: for regular students

Degree: MSci Mathematics (Masters) - University College London University

Subjects offered: Maths, Physics


“About Me Hi! My name is Pantelis and I am a 4th year student at University College London, in my favorite subject which is Mathematics. Having already faced the problems of not understanding what the lecturer means, feeling shy to a...”

MyTutor guarantee

You may also like...

Posts by Pantelis

Express (3x^2 - 3x - 2)/(x-1)(x-2) in partial fractions

Find the equation of the normal line at the point H, where θ= π/6, on the curve with equations x=3sinθ and y=5cosθ

Find the roots of the quadratic equation, x^2 - 8x + 24 = 0, by completing the square.

Suppose you are given a rectangle where the length is equal to 2x+4 and its width is equal to 3x-2. Assuming that the perimeter is equal to 54 cm, what's the value of x?

Other GCSE Maths questions

When do I use a cosine rule over a sine rule?

Find the roots of the quadratic equation, x^2 - 8x + 24 = 0, by completing the square.

Solve the equation (2x+3)/(x-4)-(2x-8)/(2x+1)=1 and give the answer to 2 decimal places

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss