SOLUTION: Find the roots of quadratic equation, if more than one, separate with commas, W^2+2W-3=0

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Question 293470: Find the roots of quadratic equation, if more than one, separate with commas,
W^2+2W-3=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

w%5E2%2B2w-3=0 Start with the given equation.


Notice that the quadratic w%5E2%2B2w-3 is in the form of Aw%5E2%2BBw%2BC where A=1, B=2, and C=-3


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-%282%29+%2B-+sqrt%28+%282%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Plug in A=1, B=2, and C=-3


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


w+=+%28-2+%2B-+sqrt%28+4--12+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-3%29 to get -12


w+=+%28-2+%2B-+sqrt%28+4%2B12+%29%29%2F%282%281%29%29 Rewrite sqrt%284--12%29 as sqrt%284%2B12%29


w+=+%28-2+%2B-+sqrt%28+16+%29%29%2F%282%281%29%29 Add 4 to 12 to get 16


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


w+=+%28-2+%2B-+4%29%2F%282%29 Take the square root of 16 to get 4.


w+=+%28-2+%2B+4%29%2F%282%29 or w+=+%28-2+-+4%29%2F%282%29 Break up the expression.


w+=+%282%29%2F%282%29 or w+=++%28-6%29%2F%282%29 Combine like terms.


w+=+1 or w+=+-3 Simplify.


So the solutions are w+=+1 or w+=+-3