Answer:
The expression 19-4x+x^2 can be written in the form (x+a)^2+b as (x - 2)^2 + 15.
In this form, a = -2 and b = 15.
Explanation:
Step 1: Rearrange the terms in descending order of powers of x.
x^2 - 4x + 19
Step 2: Take half of the coefficient of x (-4/2 = -2) and square it (-2)^2 = 4.
Step 3: Add and subtract the value obtained in step 2 inside the parentheses.
x^2 - 4x + 4 - 4 + 19
Step 4: Group the first three terms together and simplify the expression.
(x^2 - 4x + 4) - 4 + 19
(x - 2)^2 + 15