Complete the square: m^2 − 30m Then, write the result as a binomial squared.

Question

I understand how to complete the square to get a trinomial, but I'm stuck on "write the result as a binomial squared." How do I do that?

Thank you kindly for your help

Answer 1

When you complete the square you are creating a perfect square trinomial which means the trinomial can be written as a binomial squared. For example, (x+3)² = x²+6x+9. All you are being asked to do is go in the reverse direction.

Another example: x²-14x + ___ , completes the square with 49 (1/2 of -14 squared). That can be rewritten as (x - 7)². As long as the leading coefficient is 1, you take 1/2 of b and square it to complete the square, then the binomial that you square contains a 2nd term that is 1/2 of b.

(m - 15)² = m²-30m+225

Answer 2

take half of the of the linear term and square it

half of -30 = -15

square of -15 = 225

m^2 -30m +225

= (m-15)^2

in general

m^2 + bm + (b/2)^2

= (m+b/2)^2