SOLUTION: Solve p^2+4p-2=0

Algebra ->  Graphs -> SOLUTION: Solve p^2+4p-2=0      Log On


   

Question 132904: Solve

p^2+4p-2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for p:


Starting with the general quadratic

ap%5E2%2Bbp%2Bc=0

the general solution using the quadratic equation is:

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



So lets solve p%5E2%2B4%2Ap-2=0 ( notice a=1, b=4, and c=-2)




p+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A1%2A-2+%29%29%2F%282%2A1%29 Plug in a=1, b=4, and c=-2



p+=+%28-4+%2B-+sqrt%28+16-4%2A1%2A-2+%29%29%2F%282%2A1%29 Square 4 to get 16



p+=+%28-4+%2B-+sqrt%28+16%2B8+%29%29%2F%282%2A1%29 Multiply -4%2A-2%2A1 to get 8



p+=+%28-4+%2B-+sqrt%28+24+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



p+=+%28-4+%2B-+2%2Asqrt%286%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



p+=+%28-4+%2B-+2%2Asqrt%286%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

p+=+%28-4+%2B+2%2Asqrt%286%29%29%2F2 or p+=+%28-4+-+2%2Asqrt%286%29%29%2F2


Now break up the fraction


p=-4%2F2%2B2%2Asqrt%286%29%2F2 or p=-4%2F2-2%2Asqrt%286%29%2F2


Simplify


p=-2%2Bsqrt%286%29 or p=-2-sqrt%286%29


So these expressions approximate to

p=0.449489742783178 or p=-4.44948974278318


So our solutions are:
p=0.449489742783178 or p=-4.44948974278318