If a2 +  b2 + 49c2 + 18 = 2(b - 28c - a) then the value of (a + b - 7c) is:4321

The given equation is a^2 + b^2 + 49c^2 + 18 = 2(b - 28c - a).

Let's rearrange the equation:

a^2 + 2a + b^2 - 2b + 49c^2 + 2*28c + 18 = 0.

This can be rewritten as:

(a + 1)^2 + (b - 1)^2 + (7c + 1)^2 = 0.

Since the square of a real number is always non-negative, the sum of three squares equals zero only if each of the squares is zero.

So, we have:

a + 1 = 0, b - 1 = 0, and 7c + 1 = 0.

Solving these equations gives:

a = -1, b = 1, and c = -1/7.

Substituting these values into the expression for (a + b - 7c) gives:

(-1) + 1 - 7*(-1/7) = 0 + 1 = 1.

So, the value of (a + b - 7c) is 1.