SOLUTION: Can someone please help me find the x-intercepts?? I keep getting confused and space. y = x² + 5x + 1

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Question 173543: Can someone please help me find the x-intercepts?? I keep getting confused and space.
y = x² + 5x + 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-intercepts, simply set the right side equal to zero to get



x%5E2%2B5x%2B1=0


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc=0 where a=1, b=5, and c=1


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%285%29+%2B-+sqrt%28+%285%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Plug in a=1, b=5, and c=1


x+=+%28-5+%2B-+sqrt%28+25-4%281%29%281%29+%29%29%2F%282%281%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25-4+%29%29%2F%282%281%29%29 Multiply 4%281%29%281%29 to get 4


x+=+%28-5+%2B-+sqrt%28+21+%29%29%2F%282%281%29%29 Subtract 4 from 25 to get 21


x+=+%28-5+%2B-+sqrt%28+21+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-5%2Bsqrt%2821%29%29%2F%282%29 or x+=+%28-5-sqrt%2821%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%28-5%2Bsqrt%2821%29%29%2F%282%29 or x+=+%28-5-sqrt%2821%29%29%2F%282%29


which approximate to x=-0.209 or x=-4.791



So the x-intercepts are approximately (-0.209,0) and (-4.791,0)