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

becomes 

(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

PK
Answered by Pantelis K. Maths tutor

6484 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

How do you solve simultaneous equations?


How do I know when to use sine, cos or tan when working with right angled triangles?


Solve 10x - 7 > 13x +2


Find the coefficient of the constant term of the expression (2x+1/(4x^3 ))^8


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