SOLUTION: 2x^2 - 3x - 1 = 0 x^2 = 8x -5

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Question 227579: 2x^2 - 3x - 1 = 0

x^2 = 8x -5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you going




2x%5E2-3x-1=0 Start with the given equation.


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


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


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


x+=+%283+%2B-+sqrt%28+9--8+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-1%29 to get -8


x+=+%283+%2B-+sqrt%28+9%2B8+%29%29%2F%282%282%29%29 Rewrite sqrt%289--8%29 as sqrt%289%2B8%29


x+=+%283+%2B-+sqrt%28+17+%29%29%2F%282%282%29%29 Add 9 to 8 to get 17


x+=+%283+%2B-+sqrt%28+17+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%283%2Bsqrt%2817%29%29%2F%284%29 or x+=+%283-sqrt%2817%29%29%2F%284%29 Break up the expression.


So the solutions are x+=+%283%2Bsqrt%2817%29%29%2F%284%29 or x+=+%283-sqrt%2817%29%29%2F%284%29


which approximate to x=1.781 or x=-0.281