Question

Consider the following, what is the summation of all solutions? (2x+4)^2+1=5

Answer 1

Answer:

- 4

Step-by-step explanation:

(2x + 4)² + 1 = 5 ← expand left side using FOIL and simplify

4x² + 16x + 16 + 1 = 5

4x² + 16x + 17 = 5 ( subtract 5 from both sides )

4x² + 16x + 12 = 0 ( divide terms by common factor 4 )

x² + 4x + 3 = 0 ← in standard form

(x + 3)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x + 1 = 0 ⇒ x = - 1

Summation of solutions = - 3 + (- 1) = - 3 - 1 = - 4