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

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Answer 1 · 2018-05-07T02:13:48

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

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

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

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

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

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

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

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

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

How do you solve 4(x-4)^(3/2)=-64(x-4)^(3/2)=-6?