Pre-calc help: Completing the square

[celticdove_]

I've been going through some textbook questions and a question asks:
Find real numbers b and c such that the following equation holds, where a is a real number:
1800a-10a^2=-10(a-b)^2 + c
So basically I have to find out what b and c (which are constants) are. I am a bit confused and I have followed multiple videos using the completing the square method, yet I can't seem to create an equation that corresponds to the right side where I can find out what the integers b and c are. Would appreciate some help.

 

[Dr.Peterson]

This is the same as your first question. Have you learned anything from answers to that thread? And were you told to complete the square, or are you assuming that because of a comment made there? You don't need to, though you can.

Just fully expand the RHS and equate coefficients. Don't miss the fact that the LHS, in descending order, is -10a^2 + 1800a, and that fully expanding means it will be a sum of terms forming a polynomial in a.

Please show your attempts using both methods, so we can help you learn to equate coefficients and also to complete the square. We need to see where you are going wrong.