Question 296388
{{{ (x-4)^(3/2) = -6 }}}
This is the same as:
{{{((x-4)^(1/2))^3 = -6}}}
Take the cube root of both sides
{{{(x-4)^(1/2) = (-6)^(1/3)}}}
square both sides
{{{x - 4 = (-6)^(2/3)}}}
{{{x = (-6)^(2/3) + 4}}}
{{{x = -3.302 + 4}}}
{{{x = .698}}} answer
check:
{{{ (x-4)^(3/2) = -6 }}}
{{{ (.698 - 4)^(3/2) = -6 }}}
{{{ (-3.302)^(3/2) = -6}}}
{{{ -6.0002 = -6}}}
close enough