SOLUTION: Solve the equation. x^2+2x-1=0

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Question 122674: Solve the equation. x^2+2x-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%2B2%2Ax-1=0 ( notice a=1, b=2, and c=-1)




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



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



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



x+=+%28-2+%2B-+sqrt%28+8+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-2+%2B-+2%2Asqrt%282%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+=+%28-2+%2B-+2%2Asqrt%282%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-2+%2B+2%2Asqrt%282%29%29%2F2 or x+=+%28-2+-+2%2Asqrt%282%29%29%2F2


Now break up the fraction


x=-2%2F2%2B2%2Asqrt%282%29%2F2 or x=-2%2F2-2%2Asqrt%282%29%2F2


Simplify


x=-1%2Bsqrt%282%29 or x=-1-sqrt%282%29


So these expressions approximate to

x=0.414213562373095 or x=-2.41421356237309


So our solutions are:
x=0.414213562373095 or x=-2.41421356237309

Notice when we graph x%5E2%2B2%2Ax-1, we get:



when we use the root finder feature on a calculator, we find that x=0.414213562373095 and x=-2.41421356237309.So this verifies our answer