1. The problem statement, all variables and given/known data Find the speed of a particle whose relativistic kinetic energy is 40% greater than the Newtonian value for the same speed. Krel = relativistic kinetic energy Knew = Newtonian kinetic energy 2. Relevant equations Krel = (gamma - 1)mc^2 Knew = 0.5mv^2 gamma = 1/sqrt(1-x) x = v^2 / c^2 3. The attempt at a solution So I set it up as K(relativistic) = 1.4K(Newton).. because my problem was 40%. So (gamma - 1)mc^2 = 1.4 (0.5mv^2) and.. (gamma - 1) = (0.7mv^2)/mc^2 ... m's on top and bottom cancel out, then I replaced v^2/c^2 by x... (gamma - 1) = 0.7x 1/sqrt(1-x) = 0.7x + 1 1/(1-x) = (0.7x+1)^2 1 = 0.49x^2 + 14x + 1 - 0.49x^3 - 1.4x^2 - x 0 = x(-0.49x^2 - 1.09x + 0.4) Using the quadratic formula, I get either x = -3.12 or x = 0.9 Since x = v^2 / c^2, v = sqrt(x)*c So I get v = 0.9c But the answer is 0.61c. Where did I go wrong?