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make (a) the subject

2a+squareroot of 2a^2=10

  • math subject -

    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.

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