SOLUTION: Use the quadratic formula and explain each step as if you were teaching someone who had never used the method before. 3m^2 + 10m +3 = 0

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Question 108784: Use the quadratic formula and explain each step as if you were teaching someone who had never used the method before.
3m^2 + 10m +3 = 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 3%2Am%5E2%2B10%2Am%2B3=0 ( notice a=3, b=10, and c=3)





m+=+%28-10+%2B-+sqrt%28+%2810%29%5E2-4%2A3%2A3+%29%29%2F%282%2A3%29 Plug in a=3, b=10, and c=3




m+=+%28-10+%2B-+sqrt%28+100-4%2A3%2A3+%29%29%2F%282%2A3%29 Square 10 to get 100




m+=+%28-10+%2B-+sqrt%28+100%2B-36+%29%29%2F%282%2A3%29 Multiply -4%2A3%2A3 to get -36




m+=+%28-10+%2B-+sqrt%28+64+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)




m+=+%28-10+%2B-+8%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




m+=+%28-10+%2B-+8%29%2F6 Multiply 2 and 3 to get 6


So now the expression breaks down into two parts


m+=+%28-10+%2B+8%29%2F6 or m+=+%28-10+-+8%29%2F6


Lets look at the first part:


x=%28-10+%2B+8%29%2F6


m=-2%2F6 Add the terms in the numerator

m=-1%2F3 Divide


So one answer is

m=-1%2F3




Now lets look at the second part:


x=%28-10+-+8%29%2F6


m=-18%2F6 Subtract the terms in the numerator

m=-3 Divide


So another answer is

m=-3


So our solutions are:

m=-1%2F3 or m=-3