[tex]\bf 2^5\sqrt{(x+6)^3}+3=19\implies 2^5\sqrt{(x+6)^3}=16\implies \sqrt{(x+6)^3}=\cfrac{16}{2^5}
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\sqrt{(x+6)^3}=\cfrac{16}{32}\implies \sqrt{(x+6)^3}=\cfrac{1}{2}\implies \stackrel{\textit{squaring both sides}}{(x+6)^3=\left( \cfrac{1}{2} \right)^2}
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(x+6)^3=\cfrac{1^2}{2^2}\implies (x+6)^3=\cfrac{1}{4}\implies \stackrel{\textit{taking }\sqrt[3]{\qquad }\textit{ to both sides}}{x+6=\sqrt[3]{\cfrac{1}{4}}}
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x=\sqrt[3]{\cfrac{1}{4}}-6[/tex]
and if you plug that in your calculator, it'd give you -5.37003947505256341762.
