SOLUTION: 30m^2-77m-10=0

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Question 877076: 30m^2-77m-10=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
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 30%2Am%5E2-77%2Am-10=0 ( notice a=30, b=-77, and c=-10)





m+=+%28--77+%2B-+sqrt%28+%28-77%29%5E2-4%2A30%2A-10+%29%29%2F%282%2A30%29 Plug in a=30, b=-77, and c=-10




m+=+%2877+%2B-+sqrt%28+%28-77%29%5E2-4%2A30%2A-10+%29%29%2F%282%2A30%29 Negate -77 to get 77




m+=+%2877+%2B-+sqrt%28+5929-4%2A30%2A-10+%29%29%2F%282%2A30%29 Square -77 to get 5929 (note: remember when you square -77, you must square the negative as well. This is because %28-77%29%5E2=-77%2A-77=5929.)




m+=+%2877+%2B-+sqrt%28+5929%2B1200+%29%29%2F%282%2A30%29 Multiply -4%2A-10%2A30 to get 1200




m+=+%2877+%2B-+sqrt%28+7129+%29%29%2F%282%2A30%29 Combine like terms in the radicand (everything under the square root)




m+=+%2877+%2B-+sqrt%287129%29%29%2F%282%2A30%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




m+=+%2877+%2B-+sqrt%287129%29%29%2F60 Multiply 2 and 30 to get 60


So now the expression breaks down into two parts


m+=+%2877+%2B+sqrt%287129%29%29%2F60 or m+=+%2877+-+sqrt%287129%29%29%2F60



Now break up the fraction



m=%2B77%2F60%2Bsqrt%287129%29%2F60 or m=%2B77%2F60-sqrt%287129%29%2F60



Simplify



m=77%2F60%2Bsqrt%287129%29%2F60 or m=77%2F60-sqrt%287129%29%2F60



So the solutions are:

m=77%2F60%2Bsqrt%287129%29%2F60 or m=77%2F60-sqrt%287129%29%2F60





Note: You can also write the final answers as m+=+%2877%2Bsqrt%287129%29%29%2F60 or m+=+%2877-sqrt%287129%29%29%2F60

You can condense that into m+=+%2877%2B-sqrt%287129%29%29%2F60

These are exact answers. To find the approximate answers, use a calculator to evaluate the expressions.