SOLUTION: p squared+5p-5=0

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Question 86228: p squared+5p-5=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets solve this using the quadratic formula:

Starting with the general quadratic

ap%5E2%2Bbp%2Bc

the general form of 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%2B5%2Ap-5

p+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A-5+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=-5



p+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A-5+%29%29%2F%282%2A1%29 Square 5 to get 25



p+=+%28-5+%2B-+sqrt%28+25%2B20+%29%29%2F%282%2A1%29 Multiply -4%2A-5%2A1 to get 20



p+=+%28-5+%2B-+sqrt%28+45+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



p+=+%28-5+%2B-+3%2Asqrt%285%29%29%2F%282%2A1%29 Simplify the square root



p+=+%28-5+%2B-+3%2Asqrt%285%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

p+=+%28-5+%2B+3%2Asqrt%285%29%29%2F2 or p+=+%28-5+-+3%2Asqrt%285%29%29%2F2


Which approximate to

p=0.854101966249685 or p=-5.85410196624968


So our solutions are:
p=0.854101966249685 or p=-5.85410196624968

Notice when we graph p%5E2%2B5%2Ap-5 we get:



when we use the root finder feature on our calculator, we find that p=0.854101966249685 and p=-5.85410196624968.So this verifies our answer