Question 1193971
Make K the subject in the equation 
T = square root of (2Ksq / 0.5S-K)
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{{{T = sqrt(2K^2/(0.5S - K))}}}
{{{T^2 = 2K^2/(0.5S - K)}}}
{{{T^2*(0.5S - K) = 2K^2}}}
{{{0.5S*T^2 - T^2*K = 2K^2}}}
{{{2K^2 + K*T^2 - 0.5S*T^2 = 0}}}
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Solve the quadratic:
{{{K = -T^2/4 + sqrt(T^4 + 4S*T^2)/4}}}
{{{K = -T^2/4 + T*sqrt(T^2 + 4S)/4}}}
{{{K = -T^2/4 - T*sqrt(T^2 + 4S)/4}}}