SOLUTION: I am having problems with this one x^2+7x-1=0

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Question 102535: I am having problems with this one
x^2+7x-1=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 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%2B7%2Ax-1=0 ( notice a=1, b=7, and c=-1)




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



x+=+%28-7+%2B-+sqrt%28+49-4%2A1%2A-1+%29%29%2F%282%2A1%29 Square 7 to get 49



x+=+%28-7+%2B-+sqrt%28+49%2B4+%29%29%2F%282%2A1%29 Multiply -4%2A-1%2A1 to get 4



x+=+%28-7+%2B-+sqrt%28+53+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-7+%2B-+sqrt%2853%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-7+%2B-+sqrt%2853%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-7+%2B+sqrt%2853%29%29%2F2 or x+=+%28-7+-+sqrt%2853%29%29%2F2


Now break up the fraction


x=-7%2F2%2Bsqrt%2853%29%2F2 or x=-7%2F2-sqrt%2853%29%2F2


Simplify


x=-7+%2F+2%2Bsqrt%2853%29%2F2 or x=-7+%2F+2-sqrt%2853%29%2F2


So these expressions approximate to

x=0.140054944640259 or x=-7.14005494464026


So our solutions are:
x=0.140054944640259 or x=-7.14005494464026

Notice when we graph x%5E2%2B7%2Ax-1, we get:



when we use the root finder feature on a calculator, we find that x=0.140054944640259 and x=-7.14005494464026.So this verifies our answer