If b and 7 are solutions to the equation
x² - 4x = a. find the value of a + b.

x² - 4x = a 

is a quadratic equation, and has at most 2 solutions.
It is equivalent to

x² - 4x - a = 0 

Since its two solutions are b and 7, then the left side
must factor as

(x - b)(x - 7) = 0

x² - 7x - bx + 7b = 0

Factor x out of the two middle terms:

x² + x(-7 - b) + 7b = 0

x² + (-7 - b)x + 7b = 0

Comparing that to

x² - 4x - a = 0

We equate the coefficients of x

-7 - b = -4

Solving that:

   -b = -4+7
   -b = 3
    b = -3

We also equate the constant terms:

-a = 7b

Substituting -3 for b in that

-a = 7(-3)

-a = -21

a = 21

So a + b = 21 + (-3) = 18

Edwin