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

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step-by-step explanation:

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