Posted by jam on Tuesday, September 28, 2010 at 1:02pm.
2a + sqrt(2a^2) = 10,
Isolate the radical:
2a - 10 = -sqrt(2a^2),
Square both sides:
4a^2 - 40a + 100 = 2a^2,
4a^2 - 2a^2 - 40a + 100 = 0,
2a^2 - 40a + 100 = 0,
Divide both sides by 2:
a^2 - 20a + 50 = 0,
Solve for a using the quadratic formula:
a = (20 +- sqrt(400 - 200) / 2,
(20 +- sqrt(100 * 2) / 2,
a = (20 +- 10 * sqrt(2)) / 2,
a = 10 +- 5 * sqrt(2),
a = 10 +- 7.07,
a = 17,07, and 2.93.