How to complete the square

Completing the square refers to the process of rewriting a general quadratic expression into the form of a(x+b)2 + c.For example we are asked to complete the square for 2x2+ 4x + 5. The best way to do this is to expand the expression and compare the coefficients.1:Expansiona(x+b)2 + c = ax2+2abx+ab2+c, notice that the coefficient of x2 is a, the coefficient of x is 2ab and the coefficient of x0 (constant term) is ab2+c. 2:Compare the coefficient. Since the completed square form has to be the same as the original expression, we can see that a = 2, 2ab = 4, and ab2+c = 5. We can then work out b = 1 and c = 3. The answer is therefore 2(x+1)2 + 3. If you want to check this, you can expand this and it will be 2x2+ 4x + 5.

Answered by Zitong Z. Maths tutor

4326 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Fully simplify the expression: 4 / (sqrt(8) + 4)


How do I rationalise the denominator of √2+1]/√2-1?


Factorise x^2+3x+2=0


Find the inverse of: f(x) = (2x + 3)/(x - 4)


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 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences