SOLUTION: -5r^2-3r+2=0

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Question 553142: -5r^2-3r+2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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-5r%5E2-3r%2B2=0 Start with the given equation.


Notice that the quadratic -5r%5E2-3r%2B2 is in the form of Ar%5E2%2BBr%2BC where A=-5, B=-3, and C=2


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


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


r+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%28-5%29%282%29+%29%29%2F%282%28-5%29%29 Plug in A=-5, B=-3, and C=2


r+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%28-5%29%282%29+%29%29%2F%282%28-5%29%29 Negate -3 to get 3.


r+=+%283+%2B-+sqrt%28+9-4%28-5%29%282%29+%29%29%2F%282%28-5%29%29 Square -3 to get 9.


r+=+%283+%2B-+sqrt%28+9--40+%29%29%2F%282%28-5%29%29 Multiply 4%28-5%29%282%29 to get -40


r+=+%283+%2B-+sqrt%28+9%2B40+%29%29%2F%282%28-5%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


r+=+%283+%2B-+sqrt%28+49+%29%29%2F%282%28-5%29%29 Add 9 to 40 to get 49


r+=+%283+%2B-+sqrt%28+49+%29%29%2F%28-10%29 Multiply 2 and -5 to get -10.


r+=+%283+%2B-+7%29%2F%28-10%29 Take the square root of 49 to get 7.


r+=+%283+%2B+7%29%2F%28-10%29 or r+=+%283+-+7%29%2F%28-10%29 Break up the expression.


r+=+%2810%29%2F%28-10%29 or r+=++%28-4%29%2F%28-10%29 Combine like terms.


r+=+-1 or r+=+2%2F5 Simplify.


So the solutions are r+=+-1 or r+=+2%2F5


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