SOLUTION: Please help!! The problem is 4m^2 +25=20m. This is what I have.. 4m^2- 20m+ 25=0. I used the formula b^2 - 4ac and the answer is 400-400=0. The discriminant is zero so there is o

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help!! The problem is 4m^2 +25=20m. This is what I have.. 4m^2- 20m+ 25=0. I used the formula b^2 - 4ac and the answer is 400-400=0. The discriminant is zero so there is o      Log On


   

Question 144184: Please help!! The problem is 4m^2 +25=20m.
This is what I have.. 4m^2- 20m+ 25=0. I used the formula b^2 - 4ac and the answer is 400-400=0. The discriminant is zero so there is only one answer. But I can't figure out the #.. Any help is greatly appreciated!!! Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4m%5E2%2B25=20m Start with the given equation


4m%5E2%2B25-20m=0 Subtract 20m from both sides.


4m%5E2-20m%2B25=0 Rearrange the terms


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


Starting with the general quadratic

am%5E2%2Bbm%2Bc=0

the general solution using the quadratic equation is:

m+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve 4%2Am%5E2-20%2Am%2B25=0 ( notice a=4, b=-20, and c=25)




m+=+%28--20+%2B-+sqrt%28+%28-20%29%5E2-4%2A4%2A25+%29%29%2F%282%2A4%29 Plug in a=4, b=-20, and c=25



m+=+%2820+%2B-+sqrt%28+%28-20%29%5E2-4%2A4%2A25+%29%29%2F%282%2A4%29 Negate -20 to get 20



m+=+%2820+%2B-+sqrt%28+400-4%2A4%2A25+%29%29%2F%282%2A4%29 Square -20 to get 400 (note: remember when you square -20, you must square the negative as well. This is because %28-20%29%5E2=-20%2A-20=400.)



m+=+%2820+%2B-+sqrt%28+400%2B-400+%29%29%2F%282%2A4%29 Multiply -4%2A25%2A4 to get -400



m+=+%2820+%2B-+sqrt%28+0+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)



m+=+%2820+%2B-+0%29%2F%282%2A4%29 Simplify the square root



m+=+%2820+%2B-+0%29%2F8 Multiply 2 and 4 to get 8

So now the expression breaks down into two parts

m+=+%2820+%2B+0%29%2F8 or m+=+%2820+-+0%29%2F8

Lets look at the first part:

x=%2820+%2B+0%29%2F8

m=20%2F8 Add the terms in the numerator
m=5%2F2 Divide

So one answer is
m=5%2F2



Now lets look at the second part:

x=%2820+-+0%29%2F8

m=20%2F8 Subtract the terms in the numerator
m=5%2F2 Divide

So another answer is
m=5%2F2



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Answer:

So the only solution is

m=5%2F2