SOLUTION: could someone please help me find the x intercepts? {{{y+x^2-7x-11}}}

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Question 103983: could someone please help me find the x intercepts?
y%2Bx%5E2-7x-11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-intercepts, let y=0 and solve for x


0=x%5E2-7x-11



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-11=0 ( notice a=1, b=-7, and c=-11)




x+=+%28--7+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-11+%29%29%2F%282%2A1%29 Plug in a=1, b=-7, and c=-11



x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%2A1%2A-11+%29%29%2F%282%2A1%29 Negate -7 to get 7



x+=+%287+%2B-+sqrt%28+49-4%2A1%2A-11+%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%2B44+%29%29%2F%282%2A1%29 Multiply -4%2A-11%2A1 to get 44



x+=+%287+%2B-+sqrt%28+93+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%287+%2B-+sqrt%2893%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%2893%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%287+%2B+sqrt%2893%29%29%2F2 or x+=+%287+-+sqrt%2893%29%29%2F2


Now break up the fraction


x=%2B7%2F2%2Bsqrt%2893%29%2F2 or x=%2B7%2F2-sqrt%2893%29%2F2


Simplify


x=7+%2F+2%2Bsqrt%2893%29%2F2 or x=7+%2F+2-sqrt%2893%29%2F2


So these expressions approximate to

x=8.32182538049648 or x=-1.32182538049648


So our solutions are:
x=8.32182538049648 or x=-1.32182538049648

Notice when we graph x%5E2-7%2Ax-11, we get:



when we use the root finder feature on a calculator, we find that x=8.32182538049648 and x=-1.32182538049648.So this verifies our answer