SOLUTION: Solve {{{2w^2-8w-6=(w-1)^2}}}

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Question 207735: Solve 2w%5E2-8w-6=%28w-1%29%5E2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2w%5E2-8w-6=%28w-1%29%5E2 Start with the given equation.


2w%5E2-8w-6=w%5E2-2w%2B1 FOIL


2w%5E2-8w-6-1w%5E2%2B2w-1=0 Get every term to the left side.


w%5E2-6w-7=0 Combine like terms.


Notice that the quadratic w%5E2-6w-7 is in the form of Aw%5E2%2BBw%2BC where A=1, B=-6, and C=-7


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-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%28-7%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-6, and C=-7


w+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%28-7%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


w+=+%286+%2B-+sqrt%28+36-4%281%29%28-7%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


w+=+%286+%2B-+sqrt%28+36--28+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-7%29 to get -28


w+=+%286+%2B-+sqrt%28+36%2B28+%29%29%2F%282%281%29%29 Rewrite sqrt%2836--28%29 as sqrt%2836%2B28%29


w+=+%286+%2B-+sqrt%28+64+%29%29%2F%282%281%29%29 Add 36 to 28 to get 64


w+=+%286+%2B-+sqrt%28+64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


w+=+%286+%2B-+8%29%2F%282%29 Take the square root of 64 to get 8.


w+=+%286+%2B+8%29%2F%282%29 or w+=+%286+-+8%29%2F%282%29 Break up the expression.


w+=+%2814%29%2F%282%29 or w+=++%28-2%29%2F%282%29 Combine like terms.


w+=+7 or w+=+-1 Simplify.


So the solutions are w+=+7 or w+=+-1