Write x^2+6x+14 in the form of (x+a)^2+b where a and b are constants to be determined.

Completing the square is a method that can be used to solve the quadratic equation x^2+6x+14 in the form of (x+a)^2+b. The way we find a and b is as follows:For constant a, is found by halving the coefficient of x, so that a=6/2 where a=3For constant b, is found by taking the constant at the end of the quadratic, +14, and subtracting a^2 from it,so that b=14 - a^2 =14 - (3)^2 = 14 - 9 = 5 Now , let a=3 and b=5 and we can substitute them in the form of (x+a)^2+b Thus, the result for completing the square is:x^2+6x+14=(x+3)^2+5 Finally, we can check if the answer is true by (i) making sure that when we expand the result is equal to the quadratic equation(ii) substituting x with a number(1,2,3,..etc) and the result should be equal in both sides, LHS=RHS e.g let x=1, x^2+6x+14=(x+3)^2+5 (1)^2+6(1)+14=(1+3)^2+5 21=21 Therefore, is true.

CD
Answered by Chara D. Maths tutor

8620 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Solve these simultaneous questions: 2y+x =8 and y-2x = -1.


If x^2-5x+6=0, solve for x.


Solve the simultaneous equations: y=x^2+4x-2, y=x+2


Plot the graph for y = 4x - 3


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning