SOLUTION: 5b^2+28b+32=0

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Question 557456: 5b^2+28b+32=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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5b%5E2%2B28b%2B32=0 Start with the given equation.


Notice that the quadratic 5b%5E2%2B28b%2B32 is in the form of Ab%5E2%2BBb%2BC where A=5, B=28, and C=32


Let's use the quadratic formula to solve for "b":


b+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


b+=+%28-%2828%29+%2B-+sqrt%28+%2828%29%5E2-4%285%29%2832%29+%29%29%2F%282%285%29%29 Plug in A=5, B=28, and C=32


b+=+%28-28+%2B-+sqrt%28+784-4%285%29%2832%29+%29%29%2F%282%285%29%29 Square 28 to get 784.


b+=+%28-28+%2B-+sqrt%28+784-640+%29%29%2F%282%285%29%29 Multiply 4%285%29%2832%29 to get 640


b+=+%28-28+%2B-+sqrt%28+144+%29%29%2F%282%285%29%29 Subtract 640 from 784 to get 144


b+=+%28-28+%2B-+sqrt%28+144+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


b+=+%28-28+%2B-+12%29%2F%2810%29 Take the square root of 144 to get 12.


b+=+%28-28+%2B+12%29%2F%2810%29 or b+=+%28-28+-+12%29%2F%2810%29 Break up the expression.


b+=+%28-16%29%2F%2810%29 or b+=++%28-40%29%2F%2810%29 Combine like terms.


b+=+-8%2F5 or b+=+-4 Simplify.


So the solutions are b+=+-8%2F5 or b+=+-4

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