SOLUTION: solve by the quadractic formula. simplify your answers x^2-3x-1=0

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Question 625687: solve by the quadractic formula. simplify your answers x^2-3x-1=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
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x%5E2-3x-1=0 Start with the given equation.


Notice that the quadratic x%5E2-3x-1 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-3, 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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-1%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-3, and C=-1


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-1%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%281%29%28-1%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--4+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-1%29 to get -4


x+=+%283+%2B-+sqrt%28+9%2B4+%29%29%2F%282%281%29%29 Rewrite sqrt%289--4%29 as sqrt%289%2B4%29


x+=+%283+%2B-+sqrt%28+13+%29%29%2F%282%281%29%29 Add 9 to 4 to get 13


x+=+%283+%2B-+sqrt%28+13+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%283%2Bsqrt%2813%29%29%2F%282%29 or x+=+%283-sqrt%2813%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%283%2Bsqrt%2813%29%29%2F%282%29 or x+=+%283-sqrt%2813%29%29%2F%282%29

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