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2b² +11b=40
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Answer:

b = -8, 2.5

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.

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