Answer:
C
Explanation:
12 = - 7x - x² ( add x² to both sides )
x² + 12 = - 7x ( add 7x to both sides )
x² + 7x + 12 = 0 ← in standard form
consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)
the factors are + 4 and + 3 , then
(x + 4)(x + 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x + 3 = 0 ⇒ x = - 3
solutions are x = - 4 and x = - 3
with a = - 4 and b = - 3
then
a² + b² + a + b
= (- 4)² + (- 3)² + (- 4) + (- 3)
= 16 + 9 - 4 - 3
= 25 - 7
= 18