SOLUTION: Solve. x squared - 6x - 3 = 0

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Question 124660: Solve.
x squared - 6x - 3 = 0
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%5E2-6%2Ax-3=0 ( notice a=1, b=-6, and c=-3)




x+=+%28--6+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29 Plug in a=1, b=-6, and c=-3



x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A-3+%29%29%2F%282%2A1%29 Negate -6 to get 6



x+=+%286+%2B-+sqrt%28+36-4%2A1%2A-3+%29%29%2F%282%2A1%29 Square -6 to get 36 (note: remember when you square -6, you must square the negative as well. This is because %28-6%29%5E2=-6%2A-6=36.)



x+=+%286+%2B-+sqrt%28+36%2B12+%29%29%2F%282%2A1%29 Multiply -4%2A-3%2A1 to get 12



x+=+%286+%2B-+sqrt%28+48+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%286+%2B-+4%2Asqrt%283%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+=+%286+%2B-+4%2Asqrt%283%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%286+%2B+4%2Asqrt%283%29%29%2F2 or x+=+%286+-+4%2Asqrt%283%29%29%2F2


Now break up the fraction


x=%2B6%2F2%2B4%2Asqrt%283%29%2F2 or x=%2B6%2F2-4%2Asqrt%283%29%2F2


Simplify


x=3%2B2%2Asqrt%283%29 or x=3-2%2Asqrt%283%29


So these expressions approximate to

x=6.46410161513775 or x=-0.464101615137754


So our solutions are:
x=6.46410161513775 or x=-0.464101615137754

Notice when we graph x%5E2-6%2Ax-3, we get:



when we use the root finder feature on a calculator, we find that x=6.46410161513775 and x=-0.464101615137754.So this verifies our answer