How do you solve #4(x-4)^(3/2)=-6#?

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Answer 1 · 2018-05-07T02:13:48

#color(purple)(x = 4 + root3 (9/4)#

#4 (x-4)^(3/2) = -6#

#color(blue)("Squaring both sides"#,

#(4(x-4)^(3/2))^2 = (-6)^2#

#4^2 * (x-4)^((3 * 2)/2) = 36#

#4^2 * (x-4)^3 = 36#

#(x-4)^3 = 36 / 16 = 9 / 4#

#x - 4 = (9/4)^(1/3), " taking cube root on both sides"#

#color(purple)(x = 4 + root3 (9/4)#