SOLUTION: Can someone please help me with solving this problem? Thank you. Find the x-intercepts. y = x^2 – 7x – 2

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Question 90108: Can someone please help me with solving this problem? Thank you.
Find the x-intercepts.
y = x^2 – 7x – 2
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%5E2-7%2Ax-2=0 ( notice a=1, b=-7, and c=-2)

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



x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-2+%29%29%2F%282%2A1%29 Negate -7 to get 7



x+=+%287+%2B-+sqrt%28+49-4%2A1%2A-2+%29%29%2F%282%2A1%29 Square -7 to get 49 (note: remember when you square -7, you must square the negative as well. This is because %28-7%29%5E2=-7%2A-7=49.)



x+=+%287+%2B-+sqrt%28+49%2B8+%29%29%2F%282%2A1%29 Multiply -4%2A-2%2A1 to get 8



x+=+%287+%2B-+sqrt%28+57+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%287+%2B-+sqrt%2857%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+=+%287+%2B-+sqrt%2857%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%287+%2B+sqrt%2857%29%29%2F2 or x+=+%287+-+sqrt%2857%29%29%2F2


Now break up the fraction


x=%2B7%2F2%2Bsqrt%2857%29%2F2 or x=%2B7%2F2-sqrt%2857%29%2F2


Simplify


x=7+%2F+2%2Bsqrt%2857%29%2F2 or x=7+%2F+2-sqrt%2857%29%2F2


So these expressions approximate to

x=7.27491721763537 or x=-0.274917217635375


So our solutions are:
x=7.27491721763537 or x=-0.274917217635375

Notice when we graph x%5E2-7%2Ax-2, we get:



when we use the root finder feature on a calculator, we find that x=7.27491721763537 and x=-0.274917217635375.So this verifies our answer