SOLUTION: w^2 - 3w + 5 = 0

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Question 242790: w^2 - 3w + 5 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

w%5E2-3w%2B5=0 Start with the given equation.


Notice that the quadratic w%5E2-3w%2B5 is in the form of Aw%5E2%2BBw%2BC where A=1, B=-3, and C=5


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%285%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-3, and C=5


w+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%285%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


w+=+%283+%2B-+sqrt%28+9-4%281%29%285%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


w+=+%283+%2B-+sqrt%28+9-20+%29%29%2F%282%281%29%29 Multiply 4%281%29%285%29 to get 20


w+=+%283+%2B-+sqrt%28+-11+%29%29%2F%282%281%29%29 Subtract 20 from 9 to get -11


w+=+%283+%2B-+sqrt%28+-11+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


w+=+%283+%2B-+i%2Asqrt%2811%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


w+=+%283%2Bi%2Asqrt%2811%29%29%2F%282%29 or w+=+%283-i%2Asqrt%2811%29%29%2F%282%29 Break up the expression.


So the solutions are w+=+%283%2Bi%2Asqrt%2811%29%29%2F%282%29 or w+=+%283-i%2Asqrt%2811%29%29%2F%282%29