SOLUTION: I am having problems with this one x^2=-5x-5

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Question 102534: I am having problems with this one
x^2=-5x-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2=-5x-5 Start with the given quadratic


0=-x%5E2-5x-5 Subtract x%5E2 from both sides


Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

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



So lets solve -x%5E2-5%2Ax-5=0 ( notice a=-1, b=-5, and c=-5)




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



x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A-1%2A-5+%29%29%2F%282%2A-1%29 Negate -5 to get 5



x+=+%285+%2B-+sqrt%28+25-4%2A-1%2A-5+%29%29%2F%282%2A-1%29 Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because %28-5%29%5E2=-5%2A-5=25.)



x+=+%285+%2B-+sqrt%28+25%2B-20+%29%29%2F%282%2A-1%29 Multiply -4%2A-5%2A-1 to get -20



x+=+%285+%2B-+sqrt%28+5+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)



x+=+%285+%2B-+sqrt%285%29%29%2F%282%2A-1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%285+%2B-+sqrt%285%29%29%2F-2 Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

x+=+%285+%2B+sqrt%285%29%29%2F-2 or x+=+%285+-+sqrt%285%29%29%2F-2


Now break up the fraction


x=%2B5%2F-2%2Bsqrt%285%29%2F-2 or x=%2B5%2F-2-sqrt%285%29%2F-2


Simplify


x=-5+%2F+2-sqrt%285%29%2F2 or x=-5+%2F+2%2Bsqrt%285%29%2F2


So these expressions approximate to

x=-3.61803398874989 or x=-1.38196601125011


So our solutions are:
x=-3.61803398874989 or x=-1.38196601125011

Notice when we graph -x%5E2-5%2Ax-5, we get:



when we use the root finder feature on a calculator, we find that x=-3.61803398874989 and x=-1.38196601125011.So this verifies our answer