SOLUTION: how do I solve w²-3w+11

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Question 880977: how do I solve w²-3w+11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you meant to say w%5E2+-+3w+%2B+11=0

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for w:


Starting with the general quadratic


aw%5E2%2Bbw%2Bc=0


the general solution using the quadratic equation is:


w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve w%5E2-3%2Aw%2B11=0 ( notice a=1, b=-3, and c=11)





w+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A11+%29%29%2F%282%2A1%29 Plug in a=1, b=-3, and c=11




w+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A11+%29%29%2F%282%2A1%29 Negate -3 to get 3




w+=+%283+%2B-+sqrt%28+9-4%2A1%2A11+%29%29%2F%282%2A1%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)




w+=+%283+%2B-+sqrt%28+9%2B-44+%29%29%2F%282%2A1%29 Multiply -4%2A11%2A1 to get -44




w+=+%283+%2B-+sqrt%28+-35+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




w+=+%283+%2B-+i%2Asqrt%2835%29%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




w+=+%283+%2B-+i%2Asqrt%2835%29%29%2F%282%29 Multiply 2 and 1 to get 2




After simplifying, the quadratic has roots of


w=3%2F2%2Bsqrt%2835%29%2F2%2Ai or w=3%2F2-sqrt%2835%29%2F2%2Ai





Note: i+=+sqrt%28-1%29