What is the sum of the 2 real solutions to the equation

x=6-X2?

A. 6

B. 2

C. 1

D. - 1

E. - 6

D

Step-by-step explanation:

Given

x = 6 - x² (subtract 6 - x² from both sides)

x² + x - 6 = 0 ← in standard form

Consider the factors of the constant term ( - 6) which sum to give the coefficient of the x - term ( + 1)

The factors are + 3 and - 2, since

- 3 * 2 = - 6 and 3 - 2 = + 1, thus

(x + 3) (x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

Sum of solutions = - 3 + 2 = - 1 → D