Question

2x^2+9x=-7 Solve round to nearest tenth

Answer 1

Answer:

  x = -3.5 or -1

Step-by-step explanation:

Add 7 and factor.

  2x^2 +9x +7 = 0

  (2x +7)(x +1) = 0

  x = -3.5   or   x = -1 . . . . . values that make the factors zero

_____

Comment on factoring

Factoring ax^2 +bx +c = 0 requires you find factors of ac that have a sum of b. Here, you're looking for factors of 2·7 = 14 that have a sum of 9. If you're observant, you realize that 2+7=9, so 2 and 7 are the factors you want.

Now, you can write the factored form as ...

  (ax +p)(ax +q)/a = 0 . . . . where p and q are the factors of ac we just found

The divisor "a" is used to simplify one or both of the factors. Here, we have ...

  (2x +2)(2x +7)/2 = 0

  (x +1)(2x +7) = 0 . . . . . . we removed a factor of 2 from the first binomial