Completing the Square : Theory

• • We can use completing the square to factorise quadratics 
  • To complete the square, we take a quadratic, and we rearrange it into the form (x -a)² + b 
  • a and b can be any positive or negative numbers
• • We always make sure the quadratic is in the standard format ax² + bx + c 
  • We always half the coefficient of b, and use the format (x - b/2)² 
  • We then expand the bracket, and we should get the first 2 parts of the quadratic, ax² + bx 
  • However, the term on the end, e.g d , will be different from the term at the end in the first quadratic e.g. c 
  • So, we find the difference between d and c , and then we add it to the format (x - b/2)² 
  • (x - b/2)² + d - c → This looks like (x - a)² + b