23x = -3x^2 + 8
3x^2 + 23x - 8 = 0
3x^2 + 24x - x - 8 = 0
3x (x + 8) -1 (x + 8) = 0
(x + 8) (3x - 1) = 0
x = -8 or x = 1/3
Answer:
8, 9, 10
Step-by-step explanation:
three positive consecutive integers
x, x + 1, x + 2
the product of the smallest and the largest is 26 more than six times the middle integer
x(x + 2) = 6(x + 1) + 26
Expand
x^2 + 2x = 6x + 6 + 26
Combine like terms
x^2 + 2x = 6x + 32
Subtract 6x + 32 from both sides
x^2 - 4x - 32 = 0
Factor
(Alternately use the quadratic formula or complete the sqaure)
(x - 8)(x + 4)
x = {-4, 8}
-4 is extraneous because the integers must be positive
x = 8
x + 1 = 9
x + 2 = 10
8, 9, 10