SOLUTION: Solve x^2+7x+2=0 Any help appreciated

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Question 89173: Solve
x^2+7x+2=0
Any help appreciated
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%2B2=0 ( notice a=1, b=7, and c=2)

x+=+%28-7+%2B-+sqrt%28+%287%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Plug in a=1, b=7, and c=2



x+=+%28-7+%2B-+sqrt%28+49-4%2A1%2A2+%29%29%2F%282%2A1%29 Square 7 to get 49



x+=+%28-7+%2B-+sqrt%28+49%2B-8+%29%29%2F%282%2A1%29 Multiply -4%2A2%2A1 to get -8



x+=+%28-7+%2B-+sqrt%28+41+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-7+%2B-+sqrt%2841%29%29%2F%282%2A1%29 Simplify the square root



x+=+%28-7+%2B-+sqrt%2841%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-7+%2B+sqrt%2841%29%29%2F2 or x+=+%28-7+-+sqrt%2841%29%29%2F2


which split up to


x=-7%2F2%2Bsqrt%2841%29%2F2 or x=-7%2F2-sqrt%2841%29%2F2




Which approximate to

x=-0.298437881283576 or x=-6.70156211871642


So our solutions are:
x=-0.298437881283576 or x=-6.70156211871642

Notice when we graph x%5E2%2B7%2Ax%2B2, we get:



when we use the root finder feature on a calculator, we find that x=-0.298437881283576 and x=-6.70156211871642.So this verifies our answer