SOLUTION: 1/2x^2 - x -2 =0 answer: x= 1+- sqrt(5) im not good with fractons trying to figure out how my book got this answer

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Question 185542: 1/2x^2 - x -2 =0

answer: x= 1+- sqrt(5)


im not good with fractons trying to figure out how my book got this answer
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F2%29x%5E2+-+x+-2+=0 Start with the given equation.


x%5E2+-+2x+-4+=0 Multiply EVERY term by the LCD 2 to clear the fractions.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-2, and c=-4


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-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-2, and c=-4


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


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


x+=+%282+%2B-+sqrt%28+4--16+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-4%29 to get -16


x+=+%282+%2B-+sqrt%28+4%2B16+%29%29%2F%282%281%29%29 Rewrite sqrt%284--16%29 as sqrt%284%2B16%29


x+=+%282+%2B-+sqrt%28+20+%29%29%2F%282%281%29%29 Add 4 to 16 to get 20


x+=+%282+%2B-+sqrt%28+20+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%282+%2B-+2%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%29%2F%282%29+%2B-+%282%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+1+%2B-+sqrt%285%29 Reduce.



So the solutions are x+=+1+%2B-+sqrt%285%29


This really means that the solutions are x+=+1%2Bsqrt%285%29 or x+=+1-sqrt%285%29 (since the symbol tells you that you have a "plus" or a "minus" in the place of the )