SOLUTION: squareroot of negative w then subracting 6=w

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Question 200506: squareroot of negative w then subracting 6=w
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28-w%29-6=w Start with the given equation.


sqrt%28-w%29=w%2B6 Add 6 to both sides.


-w=%28w%2B6%29%5E2 Square both sides


-w=w%5E2%2B12w%2B36 FOIL


0=w%5E2%2B12w%2B36%2Bw Add w to both sides.


0=w%5E2%2B13w%2B36 Combine like terms.


Notice that the quadratic w%5E2%2B13w%2B36 is in the form of Aw%5E2%2BBw%2BC where A=1, B=13, and C=36


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-%2813%29+%2B-+sqrt%28+%2813%29%5E2-4%281%29%2836%29+%29%29%2F%282%281%29%29 Plug in A=1, B=13, and C=36


w+=+%28-13+%2B-+sqrt%28+169-4%281%29%2836%29+%29%29%2F%282%281%29%29 Square 13 to get 169.


w+=+%28-13+%2B-+sqrt%28+169-144+%29%29%2F%282%281%29%29 Multiply 4%281%29%2836%29 to get 144


w+=+%28-13+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Subtract 144 from 169 to get 25


w+=+%28-13+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


w+=+%28-13+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


w+=+%28-13+%2B+5%29%2F%282%29 or w+=+%28-13+-+5%29%2F%282%29 Break up the expression.


w+=+%28-8%29%2F%282%29 or w+=++%28-18%29%2F%282%29 Combine like terms.


w+=+-4 or w+=+-9 Simplify.


So the possible solutions are w+=+-4 or w+=+-9


However, if you plug in w+=+-9, you get an inconsistent equation.


So the only solution is w+=+-4