SOLUTION: 2h^2-h-3=0

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Question 200756: 2h^2-h-3=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


Notice that the quadratic 2h%5E2-h-3 is in the form of Ah%5E2%2BBh%2BC where A=2, B=-1, and C=-3


Let's use the quadratic formula to solve for "h":


h+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


h+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%282%29%28-3%29+%29%29%2F%282%282%29%29 Plug in A=2, B=-1, and C=-3


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


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


h+=+%281+%2B-+sqrt%28+1--24+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-3%29 to get -24


h+=+%281+%2B-+sqrt%28+1%2B24+%29%29%2F%282%282%29%29 Rewrite sqrt%281--24%29 as sqrt%281%2B24%29


h+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%282%29%29 Add 1 to 24 to get 25


h+=+%281+%2B-+sqrt%28+25+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


h+=+%281+%2B-+5%29%2F%284%29 Take the square root of 25 to get 5.


h+=+%281+%2B+5%29%2F%284%29 or h+=+%281+-+5%29%2F%284%29 Break up the expression.


h+=+%286%29%2F%284%29 or h+=++%28-4%29%2F%284%29 Combine like terms.


h+=+3%2F2 or h+=+-1 Simplify.


So the solutions are h+=+3%2F2 or h+=+-1