SOLUTION: What is 2m^2+9m+7=3

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Question 600343: What is 2m^2+9m+7=3
Found 2 solutions by jim_thompson5910, w_parminder:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2m%5E2%2B9m%2B7=3 Start with the given equation.


2m%5E2%2B9m%2B7-3=0 Subtract 3 from both sides.


2m%5E2%2B9m%2B4=0 Combine like terms.


Notice we have a quadratic equation in the form of am%5E2%2Bbm%2Bc where a=2, b=9, and c=4


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-%289%29+%2B-+sqrt%28+%289%29%5E2-4%282%29%284%29+%29%29%2F%282%282%29%29 Plug in a=2, b=9, and c=4


m+=+%28-9+%2B-+sqrt%28+81-4%282%29%284%29+%29%29%2F%282%282%29%29 Square 9 to get 81.


m+=+%28-9+%2B-+sqrt%28+81-32+%29%29%2F%282%282%29%29 Multiply 4%282%29%284%29 to get 32


m+=+%28-9+%2B-+sqrt%28+49+%29%29%2F%282%282%29%29 Subtract 32 from 81 to get 49


m+=+%28-9+%2B-+sqrt%28+49+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


m+=+%28-9+%2B-+7%29%2F%284%29 Take the square root of 49 to get 7.


m+=+%28-9+%2B+7%29%2F%284%29 or m+=+%28-9+-+7%29%2F%284%29 Break up the expression.


m+=+%28-2%29%2F%284%29 or m+=++%28-16%29%2F%284%29 Combine like terms.


m+=+-1%2F2 or m+=+-4 Simplify.


So the answers are m+=+-1%2F2 or m+=+-4


Answer by w_parminder(53) About Me  (Show Source):
You can put this solution on YOUR website!
2m%5E2%2B9m%2B7=3
or 2m%5E2%2B9m%2B7-3=0
or 2m%5E2%2B9m%2B4=0
Now this quadratic equation can be solved using the formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
But I solve it by splitting its middle term
So 2m%5E2%2B9m%2B4=0 can be written as
2m%5E2%2B8m%2Bm%2B4=0
OR %28+2m%5E2%2B8m+%29+%2B+%28+m%2B4+%29=0
OR 2m%2A%28+m%2B4+%29+%2B+1%2A%28+m%2B4+%29
OR %28+m%2B4+%29%28+2m%2B1+%29=0
Now either (m + 4) = 0 OR (2m + 1) = 0
solving these equations we get,
m = -4 & m = -1/2