How do you solve an equation by completing the square?

Firstly, you can only complete the square on quadratic functions (functions in the form Ax2+Bx+C)

If A=1,

Consider B, the coefficient of x. Substitute it into ( x + (B/2) )2

We know if we multiply this out, we will get x2+Bx+(B/2)2

However, we want x2+Bx+C. 

We therefore subtract the (B/2)2 we don't want and add the C we do. 

This gives us ( x + (B/2) )2 - (B/2)2 + C. 

This method is called 'completing the sqaure'

If A does not = 1, manipulate the quadratic so it is in the form A( x+ (B/A) x + (C/A))Solve the bracket as normal and multiply through by A at the end.

 

 

Answered by Emma J. Maths tutor

4501 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the area under the curve y = (4x^3) + (9x^2) - 2x + 7 between x=0 and x=2


Integrate 1/(1 - 3*x) with respect to x


On the same diagram, sketch the graphs of: y = |5x -2| and y = |2x| and hence solve the equation |5x - 2| = |2x|


Differentiate 7(3x^2+7)^(1/3)


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