6x-11x to the power of 1/2 + 4 = 0

Question

I am unsure how to do this exation with the power to a half. Please help!!

Answer 1

6x-11x^½+4=0 is the same as 6x-11√x+4=0,

6x+4=11√x, square both sides:

(6x+4)²=121x,

36x²+48x+16=121x,

36x²-73x+16=0=(4x-1)(9x-16), which gives us two possible solutions: x=¼ or 16/9.

√x=½ or 4/3, so we need to test these by substituting into 6x-11x^½+4:

x=¼: 6/4-11/2+4=3/2-11/2+4=-8/2+4=-4+4=0, so x=¼ is a solution.

x=16/9: 96/9-44/3+4=32/3-44/3+4=-12/3+4=-4+4=0, so x=16/9 is also a solution.

ANSWER: x=¼ or 16/9.