Question

Please complete the square, show your work.
x^2 - 19x +c

Answer 1

Explanation:

We need to transform the given x^2 - 19x + c into the form

(x - a)^2 + d

by completing the square:

1. Take half of the coefficient (-19) of x, obtaining -19/2.

2. Square this result, obtaining 361/4.

3. Add this to x^2 - 19x, and then immediately subtract it:

x^2 - 19x + c becomes x^2 - 19x + 361/4 - 361/4+ c

4. Replace the first three terms with (x - 19/2)^2:

x^2 - 19x + 361/4 - 361/4+ c => (x - 19/2)^2 - 361/4 + c

5. Put this into final form: (x - 19/2)^2 - (361/4 - c)