Question

2b² +11b=40 Help please

Answer 1

9514 1404 393

Answer:

  b = -8, 2.5

Step-by-step explanation:

The equation can be rewritten to standard form:

  2b² +11b -40 = 0

In this form, it can be factored by looking for factors of (2)(-40) that have a total of +11.

  -80 = 80(-1) = 40(-2) = 20(-4) = 16(-5) = 10(-8)

The factors 16 and -5 total 11, so we can now write the equation in a form suitable for factoring by grouping:

  2b² +16b -5b -40 = 0 . . . . write the b term using the numbers we found

  2b(b +8) -5(b +8) = 0 . . . . factor pairs of terms

  (2b -5)(b +8) = 0 . . . . . . . . finish the factoring

Solutions are values of b that make these factors zero:

  2b -5 = 0  ⇒  b = 5/2

  b +8 = 0  ⇒  b = -8

Solution to the equation are b = -8 and b = 5/2.