SOLUTION: find the x-intercepts y=x^2-3x-1

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Question 110955: find the x-intercepts
y=x^2-3x-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
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%5E2-3%2Ax-1=0 ( notice a=1, b=-3, and c=-1)





x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29 Plug in a=1, b=-3, and c=-1




x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A-1+%29%29%2F%282%2A1%29 Negate -3 to get 3




x+=+%283+%2B-+sqrt%28+9-4%2A1%2A-1+%29%29%2F%282%2A1%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)




x+=+%283+%2B-+sqrt%28+9%2B4+%29%29%2F%282%2A1%29 Multiply -4%2A-1%2A1 to get 4




x+=+%283+%2B-+sqrt%28+13+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%283+%2B-+sqrt%2813%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+=+%283+%2B-+sqrt%2813%29%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%283+%2B+sqrt%2813%29%29%2F2 or x+=+%283+-+sqrt%2813%29%29%2F2



Now break up the fraction



x=%2B3%2F2%2Bsqrt%2813%29%2F2 or x=%2B3%2F2-sqrt%2813%29%2F2



Simplify



x=3%2F2%2Bsqrt%2813%29%2F2 or x=3%2F2-sqrt%2813%29%2F2



So the solutions are:

x=3%2F2%2Bsqrt%2813%29%2F2 or x=3%2F2-sqrt%2813%29%2F2