SOLUTION: Solve by using Quadratic formula t^(2)+7t+4=0

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Question 248273: Solve by using Quadratic formula t^(2)+7t+4=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 t:


Starting with the general quadratic


at%5E2%2Bbt%2Bc=0


the general solution using the quadratic equation is:


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




So lets solve t%5E2%2B7%2At%2B4=0 ( notice a=1, b=7, and c=4)





t+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29 Plug in a=1, b=7, and c=4




t+=+%28-7+%2B-+sqrt%28+49-4%2A1%2A4+%29%29%2F%282%2A1%29 Square 7 to get 49




t+=+%28-7+%2B-+sqrt%28+49%2B-16+%29%29%2F%282%2A1%29 Multiply -4%2A4%2A1 to get -16




t+=+%28-7+%2B-+sqrt%28+33+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




t+=+%28-7+%2B-+sqrt%2833%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




t+=+%28-7+%2B-+sqrt%2833%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


t+=+%28-7+%2B+sqrt%2833%29%29%2F2 or t+=+%28-7+-+sqrt%2833%29%29%2F2



Now break up the fraction



t=-7%2F2%2Bsqrt%2833%29%2F2 or t=-7%2F2-sqrt%2833%29%2F2



Simplify



t=-7%2F2%2Bsqrt%2833%29%2F2 or t=-7%2F2-sqrt%2833%29%2F2



So the solutions are:

t=-7%2F2%2Bsqrt%2833%29%2F2 or t=-7%2F2-sqrt%2833%29%2F2