SOLUTION: Solve the equation for w (w+1)^2=2w^2+6w+5

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Question 315575: Solve the equation for w
(w+1)^2=2w^2+6w+5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28w%2B1%29%5E2=2w%5E2%2B6w%2B5 Start with the given equation.


w%5E2%2B2w%2B1=2w%5E2%2B6w%2B5 FOIL


w%5E2%2B2w%2B1-2w%5E2-6w-5=0 Get every term to the left side.


-w%5E2-4w-4=0 Combine like terms.


Notice that the quadratic -w%5E2-4w-4 is in the form of Aw%5E2%2BBw%2BC where A=-1, B=-4, and C=-4


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


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


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


w+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%28-1%29%28-4%29+%29%29%2F%282%28-1%29%29 Negate -4 to get 4.


w+=+%284+%2B-+sqrt%28+16-4%28-1%29%28-4%29+%29%29%2F%282%28-1%29%29 Square -4 to get 16.


w+=+%284+%2B-+sqrt%28+16-16+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%28-4%29 to get 16


w+=+%284+%2B-+sqrt%28+0+%29%29%2F%282%28-1%29%29 Subtract 16 from 16 to get 0


w+=+%284+%2B-+sqrt%28+0+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


w+=+%284+%2B-+0%29%2F%28-2%29 Take the square root of 0 to get 0.


w+=+%284+%2B+0%29%2F%28-2%29 or w+=+%284+-+0%29%2F%28-2%29 Break up the expression.


w+=+%284%29%2F%28-2%29 or w+=++%284%29%2F%28-2%29 Combine like terms.


w+=+-2 or w+=+-2 Simplify.


So the only solution is w+=+-2