Completing the square — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
Rewriting x2 + bx as a perfect square minus a constant.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Perfect square — A number that is some whole number squared: 1, 4, 9, 16, 25, …
Practise this idea
2 questions in the course bank use Completing the square, in Solving Quadratic Equations, Equations of Circles.
Problem 1
Solve x2 + 6x = 16 by completing the square.
Worked answer
2 and -8
x2 + 6x + 9 = 25
(x+3)2 = 25
x + 3 = ± 5
x = 2 or x = -8
Problem 2
Find the radius of x2 + y2 - 6x + 8y - 11 = 0.
Worked answer
6
(x-3)2 + (y+4)2 = 36
r = 6