SOLUTION: Use the quadratic formula to solve the equation. Give both exact and approximate answers. 3m2 + 12m + 5 = 0

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Question 201194: Use the quadratic formula to solve the equation. Give both exact and approximate answers.
3m2 + 12m + 5 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3m%5E2%2B12m%2B5=0 Start with the given equation.


Notice that the quadratic 3m%5E2%2B12m%2B5 is in the form of Am%5E2%2BBm%2BC where A=3, B=12, and C=5


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


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


m+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%283%29%285%29+%29%29%2F%282%283%29%29 Plug in A=3, B=12, and C=5


m+=+%28-12+%2B-+sqrt%28+144-4%283%29%285%29+%29%29%2F%282%283%29%29 Square 12 to get 144.


m+=+%28-12+%2B-+sqrt%28+144-60+%29%29%2F%282%283%29%29 Multiply 4%283%29%285%29 to get 60


m+=+%28-12+%2B-+sqrt%28+84+%29%29%2F%282%283%29%29 Subtract 60 from 144 to get 84


m+=+%28-12+%2B-+sqrt%28+84+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


m+=+%28-12+%2B-+2%2Asqrt%2821%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


m+=+%28-12%2B2%2Asqrt%2821%29%29%2F%286%29 or m+=+%28-12-2%2Asqrt%2821%29%29%2F%286%29 Break up the expression.


m+=+%28-6%2Bsqrt%2821%29%29%2F%283%29 or m+=+%28-6-sqrt%2821%29%29%2F%283%29 Reduce.


So the solutions are m+=+%28-6%2Bsqrt%2821%29%29%2F%283%29 or m+=+%28-6-sqrt%2821%29%29%2F%283%29


which approximate to m=-0.472 or m=-3.528