Let's use the quadratic formula to solve for w:
Starting with the general quadratic
the general solution using the quadratic equation is:
So lets solve ( notice , , and )
Plug in a=1, b=-3, and c=11
Negate -3 to get 3
Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because .)
Multiply to get
Combine like terms in the radicand (everything under the square root)
Simplify the square root (note: If you need help with simplifying the square root, check out this solver)
Multiply 2 and 1 to get 2
After simplifying, the quadratic has roots of
or
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